Title: | Computation of Some Important Distributional Properties |
---|---|
Description: | Generally, most of the packages specify the probability density function, cumulative distribution function, quantile function, and random numbers generation of the probability distributions. The present package allows to compute some important distributional properties, including the first four ordinary and central moments, Pearson's coefficient of skewness and kurtosis, the mean and variance, coefficient of variation, median, and quartile deviation at some parametric values of several well-known and extensively used probability distributions. |
Authors: | Christophe Chesneau [aut], Muhammad Imran [aut, cre], M.H Tahir [aut], Farrukh Jamal [aut] |
Maintainer: | Muhammad Imran <[email protected]> |
License: | GPL-2 |
Version: | 0.1.0 |
Built: | 2025-02-19 02:42:14 UTC |
Source: | https://github.com/cran/dprop |
Generally, most of the packages specify the probability density function, cumulative distribution function, quantile function, and random numbers generation of the probability distributions. The present package allows to compute some important distributional properties, including the first four ordinary and central moments, Pearson's coefficient of skewness and kurtosis, the mean and variance, coefficient of variation, median, and quartile deviation at some parametric values of several well-known and extensively used probability distributions.
Package: | dprop |
Type: | Package |
Version: | 0.1.0 |
Date: | 2023-06-28 |
License: | GPL-2 |
Muhammad Imran <[email protected]>
Christophe Chesneau <[email protected]>, Muhammad Imran <[email protected]>, M.H Tahir <[email protected]> and Farrukh Jamal <[email protected]>.
Compute the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the beta distribution.
d_beta(alpha, beta)
d_beta(alpha, beta)
alpha |
The strictly positive shape parameter of the beta distribution ( |
beta |
The strictly positive shape parameter of the beta distribution ( |
The following is the probability density function of the beta distribution:
where ,
and
.
d_beta gives the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the beta distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Gupta, A. K., & Nadarajah, S. (2004). Handbook of beta distribution and its applications. CRC Press.
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Beta distributions. Continuous univariate distributions. 2nd ed. New York, NY: John Wiley and Sons, 221-235.
d_beta(2,2)
d_beta(2,2)
Compute the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the beta exponential distribution.
d_bexp(lambda, alpha, beta)
d_bexp(lambda, alpha, beta)
lambda |
The strictly positive scale parameter of the exponential distribution ( |
alpha |
The strictly positive shape parameter of the beta distribution ( |
beta |
The strictly positive shape parameter of the beta distribution ( |
The following is the probability density function of the beta exponential distribution:
where ,
,
and
.
d_bexp gives the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the beta exponential distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Nadarajah, S., & Kotz, S. (2006). The beta exponential distribution. Reliability Engineering & System Safety, 91(6), 689-697.
d_bexp(1,1,0.2)
d_bexp(1,1,0.2)
Compute the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Birnbaum-Saunders distribution.
d_bs(v)
d_bs(v)
v |
The strictly positive scale parameter of the Birnbaum-Saunders distribution ( |
The following is the probability density function of the Birnbaum-Saunders distribution:
where and
.
d_bs gives the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Birnbaum-Saunders distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Chan, S., Nadarajah, S., & Afuecheta, E. (2016). An R package for value at risk and expected shortfall. Communications in Statistics Simulation and Computation, 45(9), 3416-3434.
d_bs(5)
d_bs(5)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Burr XII distribution.
d_burr(k, c)
d_burr(k, c)
k |
The strictly positive shape parameter of the Burr XII distribution ( |
c |
The strictly positive shape parameter of the Burr XII distribution ( |
The following is the probability density function of the Burr XII distribution:
where ,
and
.
d_burr gives the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Burr XII distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Rodriguez, R. N. (1977). A guide to the Burr type XII distributions. Biometrika, 64(1), 129-134.
Zimmer, W. J., Keats, J. B., & Wang, F. K. (1998). The Burr XII distribution in reliability analysis. Journal of Quality Technology, 30(4), 386-394.
d_burr(2,10)
d_burr(2,10)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Chen distribution.
d_chen(k, c)
d_chen(k, c)
k |
The strictly positive shape parameter of the Chen distribution ( |
c |
The strictly positive scale parameter of the Chen distribution ( |
The following is the probability density function of the Chen distribution:
where ,
and
.
d_chen gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Chen distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49(2), 155–161.
d_chen(0.2,0.2)
d_chen(0.2,0.2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the (non-central) Chi-squared distribution.
d_chi(n)
d_chi(n)
n |
It is a degree of freedom and the positive parameter of the Chi-squared distribution ( |
The following is the probability density function of the (non-central) Chi-squared distribution:
where and
.
d_chi gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the (non-central) Chi-squared distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Ding, C. G. (1992). Algorithm AS275: computing the non-central chi-squared distribution function. Journal of the Royal Statistical Society. Series C (Applied Statistics), 41(2), 478-482.
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (Vol. 289). John Wiley & Sons.
d_chi(2)
d_chi(2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponential distribution.
d_exp(alpha)
d_exp(alpha)
alpha |
The strictly positive scale parameter of the exponential distribution ( |
The following is the probability density function of the exponential distribution:
where and
.
d_exp gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponential distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Balakrishnan, K. (2019). Exponential distribution: theory, methods and applications. Routledge.
Singh, A. K. (1997). The exponential distribution-theory, methods and applications, Technometrics, 39(3), 341-341.
d_exp(2)
d_exp(2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponential extension distribution.
d_nh(alpha, beta)
d_nh(alpha, beta)
alpha |
The strictly positive parameter of the exponential extension distribution ( |
beta |
The strictly positive parameter of the exponential extension distribution ( |
The following is the probability density function of the exponential extension distribution:
where ,
and
.
d_nh gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponential extension distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Nadarajah, S., & Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543-558.
d_nh(0.5,1)
d_nh(0.5,1)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponentiated exponential distribution.
d_EE(alpha, beta)
d_EE(alpha, beta)
alpha |
The strictly positive scale parameter of the exponential distribution ( |
beta |
The strictly positive shape parameter of the exponentiated exponential distribution ( |
The following is the probability density function of the exponentiated exponential distribution:
where ,
and
.
d_EE gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponentiated exponential distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Nadarajah, S. (2011). The exponentiated exponential distribution: a survey. AStA Advances in Statistical Analysis, 95, 219-251.
Gupta, R. D., & Kundu, D. (2007). Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference, 137(11), 3537-3547.
d_EE(5,2)
d_EE(5,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponentiated Weibull distribution.
d_EW(a, beta, zeta)
d_EW(a, beta, zeta)
a |
The strictly positive shape parameter of the exponentiated Weibull distribution ( |
beta |
The strictly positive scale parameter of the baseline Weibull distribution ( |
zeta |
The strictly positive shape parameter of the baseline Weibull distribution ( |
The following is the probability density function of the exponentiated Weibull distribution:
where ,
,
and
.
d_EW gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the exponentiated Weibull distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Nadarajah, S., Cordeiro, G. M., & Ortega, E. M. (2013). The exponentiated Weibull distribution: a survey. Statistical Papers, 54, 839-877.
d_EW(1,1,0.5)
d_EW(1,1,0.5)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the F distribution.
d_F(alpha, beta)
d_F(alpha, beta)
alpha |
The strictly positive parameter of the F distribution ( |
beta |
The strictly positive parameter of the F distribution ( |
The following is the probability density function of the F distribution:
where ,
and
.
d_F gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the F distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (Vol. 289). John Wiley & Sons.
d_F(2,10)
d_F(2,10)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Frechet distribution.
d_fre(alpha, beta, zeta)
d_fre(alpha, beta, zeta)
alpha |
The parameter of the Frechet distribution ( |
beta |
The parameter of the Frechet distribution ( |
zeta |
The parameter of the Frechet distribution ( |
The following is the probability density function of the Frechet distribution:
where ,
,
and
. The Frechet distribution is also known as inverse Weibull distribution and special case of the generalized extreme value distribution.
d_fre gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Frechet distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Abbas, K., & Tang, Y. (2015). Analysis of Frechet distribution using reference priors. Communications in Statistics-Theory and Methods, 44(14), 2945-2956.
d_fre(5,1,0.5)
d_fre(5,1,0.5)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the gamma distribution.
d_gamma(alpha, beta)
d_gamma(alpha, beta)
alpha |
The strictly positive parameter of the gamma distribution ( |
beta |
The strictly positive parameter of the gamma distribution ( |
The following is the probability density function of the gamma distribution:
where ,
and
.
d_gamma the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the gamma distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Burgin, T. A. (1975). The gamma distribution and inventory control. Journal of the Operational Research Society, 26(3), 507-525.
d_gamma(2,2)
d_gamma(2,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Gompertz distribution.
d_gompertz(alpha, beta)
d_gompertz(alpha, beta)
alpha |
The strictly positive parameter of the Gompertz distribution ( |
beta |
The strictly positive parameter of the Gompertz distribution ( |
The following is the probability density function of the Gompertz distribution:
where ,
and
.
d_gompertz gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Gompertz distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Soliman, A. A., Abd-Ellah, A. H., Abou-Elheggag, N. A., & Abd-Elmougod, G. A. (2012). Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data. Computational Statistics & Data Analysis, 56(8), 2471-2485.
d_gompertz(2,2)
d_gompertz(2,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Gumbel distribution.
d_gumbel(alpha, beta)
d_gumbel(alpha, beta)
alpha |
Location parameter of the Gumbel distribution ( |
beta |
The strictly positive scale parameter of the Gumbel distribution ( |
The following is the probability density function of the Gumbel distribution:
where ,
,
and
.
d_gumbel gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Gumbel distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Gomez, Y. M., Bolfarine, H., & Gomez, H. W. (2019). Gumbel distribution with heavy tails and applications to environmental data. Mathematics and Computers in Simulation, 157, 115-129.
d_gumbel(1,2)
d_gumbel(1,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the inverse-gamma distribution.
d_ingam(alpha, beta)
d_ingam(alpha, beta)
alpha |
The strictly positive parameter of the inverse-gamma distribution ( |
beta |
The strictly positive parameter of the inverse-gamma distribution ( |
The following is the probability density function of the inverse-gamma distribution:
where ,
and
.
d_ingam gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the inverse-gamma distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Rivera, P. A., Calderín-Ojeda, E., Gallardo, D. I., & Gómez, H. W. (2021). A compound class of the inverse Gamma and power series distributions. Symmetry, 13(8), 1328.
Glen, A. G. (2017). On the inverse gamma as a survival distribution. Computational Probability Applications, 15-30.
d_ingam(5,2)
d_ingam(5,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy Burr XII distribution.
d_kburr(a, b, k, c)
d_kburr(a, b, k, c)
a |
The strictly positive parameter of the Kumaraswamy distribution ( |
b |
The strictly positive parameter of the Kumaraswamy distribution ( |
k |
The strictly positive parameter of the Burr XII distribution ( |
c |
The strictly positive parameter of the Burr XII distribution ( |
The following is the probability density function of the Kumaraswamy Burr XII distribution:
where ,
,
,
and
.
d_kburr gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy Burr XII distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Paranaiba, P. F., Ortega, E. M., Cordeiro, G. M., & Pascoa, M. A. D. (2013). The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 83(11), 2117-2143.
d_kburr(1.5,1,1,7)
d_kburr(1.5,1,1,7)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy distribution.
d_kum(alpha, beta)
d_kum(alpha, beta)
alpha |
The strictly positive parameter of the Kumaraswamy distribution ( |
beta |
The strictly positive parameter of the Kumaraswamy distribution ( |
The following is the probability density function of the Kumaraswamy distribution:
where ,
and
.
d_kum gives the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation at some parametric values based on the Kumaraswamy distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
El-Sherpieny, E. S. A., & Ahmed, M. A. (2014). On the kumaraswamy distribution. International Journal of Basic and Applied Sciences, 3(4), 372.
Mitnik, P. A. (2013). New properties of the Kumaraswamy distribution. Communications in Statistics-Theory and Methods, 42(5), 741-755.
Dey, S., Mazucheli, J., & Nadarajah, S. (2018). Kumaraswamy distribution: different methods of estimation. Computational and Applied Mathematics, 37, 2094-2111.
d_kum(2,2)
d_kum(2,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy exponential distribution.
d_kexp(lambda, a, b)
d_kexp(lambda, a, b)
a |
The strictly positive shape parameter of the Kumaraswamy distribution ( |
b |
The strictly positive shape parameter of the Kumaraswamy distribution ( |
lambda |
The strictly positive parameter of the exponential distribution ( |
The following is the probability density function of the Kumaraswamy exponential distribution:
where ,
,
and
.
d_kexp gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy exponential distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.
d_kexp(0.2,1,1)
d_kexp(0.2,1,1)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy normal distribution.
d_kumnorm(mu, sigma, a, b)
d_kumnorm(mu, sigma, a, b)
mu |
The location parameter of the normal distribution ( |
sigma |
The strictly positive scale parameter of the normal distribution ( |
a |
The strictly positive shape parameter of the Kumaraswamy distribution ( |
b |
The strictly positive shape parameter of the Kumaraswamy distribution ( |
The following is the probability density function of the Kumaraswamy normal distribution:
where ,
,
,
and
. The functions
and
, denote the probability density function and cumulative distribution function of the standard normal variable, respectively.
d_kumnorm gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Kumaraswamy normal distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.
d_kumnorm(0.2,0.2,2,2)
d_kumnorm(0.2,0.2,2,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Laplace distribution.
d_lap(alpha, beta)
d_lap(alpha, beta)
alpha |
Location parameter of the Laplace distribution ( |
beta |
The strictly positive scale parameter of the Laplace distribution ( |
The following is the probability density function of the Laplace distribution:
where ,
and
.
d_lap gives the first four ordinary moments, central moments, mean, variance, Pearson's coefficient of skewness, kurtosis, coefficient of variation, median and quartile deviation at some parametric values based on the Laplace distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Cordeiro, G. M., & Lemonte, A. J. (2011). The beta Laplace distribution. Statistics & Probability Letters, 81(8), 973-982.
d_lap(2,4)
d_lap(2,4)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the log-normal distribution.
d_lnormal(mu, sigma)
d_lnormal(mu, sigma)
mu |
The location parameter ( |
sigma |
The strictly positive scale parameter of the log-normal distribution ( |
The following is the probability density function of the log-normal distribution:
where ,
and
.
d_lnormal gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the log-normal distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous Univariate Distributions, Volume 1, Chapter 14. Wiley, New York.
d_lnormal(1,0.5)
d_lnormal(1,0.5)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the logistic distribution.
d_logis(mu, sigma)
d_logis(mu, sigma)
mu |
Location parameter of the logistic distribution ( |
sigma |
The strictly positive scale parameter of the logistic distribution ( |
The following is the probability density function of the logistic distribution:
where ,
and
.
d_logis gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the logistic distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, Volume 2 (Vol. 289). John Wiley & Sons.
d_logis(4,0.2)
d_logis(4,0.2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Lomax distribution.
d_lom(alpha, beta)
d_lom(alpha, beta)
alpha |
The strictly positive parameter of the Lomax distribution ( |
beta |
The strictly positive parameter of the Lomax distribution ( |
The following is the probability density function of the Lomax distribution:
where ,
and
.
d_lom gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Lomax distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Abd-Elfattah, A. M., Alaboud, F. M., & Alharby, A. H. (2007). On sample size estimation for Lomax distribution. Australian Journal of Basic and Applied Sciences, 1(4), 373-378.
d_lom(10,10)
d_lom(10,10)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Nakagami distribution.
d_naka(alpha, beta)
d_naka(alpha, beta)
alpha |
The strictly positive parameter of the Nakagami distribution ( |
beta |
The strictly positive parameter of the Nakagami distribution ( |
The following is the probability density function of the Nakagami distribution:
where ,
and
.
d_naka gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Nakagami distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Schwartz, J., Godwin, R. T., & Giles, D. E. (2013). Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution. Journal of Statistical Computation and Simulation, 83(3), 434-445.
d_naka(2,2)
d_naka(2,2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the normal distribution.
d_normal(alpha, beta)
d_normal(alpha, beta)
alpha |
Location parameter of the normal distribution ( |
beta |
The strictly positive scale parameter of the normal distribution ( |
The following is the probability density function of the normal distribution:
where ,
and
. The parameters
and
represent the mean and standard deviation, respectively.
d_normal gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the normal distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Patel, J. K., & Read, C. B. (1996). Handbook of the normal distribution (Vol. 150). CRC Press.
d_normal(4,0.2)
d_normal(4,0.2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Rayleigh distribution.
d_rayl(alpha)
d_rayl(alpha)
alpha |
The strictly positive parameter of the Rayleigh distribution ( |
The following is the probability density function of the Rayleigh distribution:
where ,
.
d_rayl gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Rayleigh distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.
d_rayl(2)
d_rayl(2)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Student t distribution.
d_st(v)
d_st(v)
v |
The strictly positive parameter of the Student distribution ( |
The following is the probability density function of the Student t distribution:
where and
.
d_st gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Student t distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Yang, Z., Fang, K. T., & Kotz, S. (2007). On the Student's t-distribution and the t-statistic. Journal of Multivariate Analysis, 98(6), 1293-1304.
Ahsanullah, M., Kibria, B. G., & Shakil, M. (2014). Normal and Student's t distributions and their applications (Vol. 4). Paris, France: Atlantis Press.
d_st(6)
d_st(6)
Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Weibull distribution.
d_wei(alpha, beta)
d_wei(alpha, beta)
alpha |
The strictly positive scale parameter of the Weibull distribution ( |
beta |
The strictly positive shape parameter of the Weibull distribution ( |
The following is the probability density function of the Weibull distribution:
where ,
and
.
d_wei gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Weibull distribution.
Muhammad Imran.
R implementation and documentation: Muhammad Imran [email protected].
Hallinan Jr, Arthur J. (1993). A review of the Weibull distribution. Journal of Quality Technology, 25(2), 85-93.
d_wei(2,2)
d_wei(2,2)