Distribution.df: Data Frame Summarizing Available Probability Distributions and Estimation Methods

Description

Data frame summarizing information about available probability distributions in Rand the EnvStats package, and which distributions have associated functions for estimating distribution parameters.

Usage

Distribution.df

Arguments

source

The EnvStats package.

Details

The table below summarizes the probability distributions available in Rand EnvStats. For each distribution, there are four associated functions for computing density values, percentiles, quantiles, and random numbers. The form of the names of these functions are dabb, pabb, qabb, and rabb, where abb is the abbreviated name of the distribution (see table below). These functions are described in the help file with the name of the distribution (see the first column of the table below). For example, the help file for Beta describes the behavior of dbeta, pbeta, qbeta, and rbeta. For most distributions, there is also an associated function for estimating the distribution parameters, and the form of the names of these functions is eabb, where abb is the abbreviated name of the distribution (see table below). All of these functions are listed in the help file Estimating Distribution Parameters. For example, the function ebeta estimates the shape parameters of a Beta distribution based on a random sample of observations from this distribution. For some distributions, there are functions to estimate distribution parameters based on Type I censored data. The form of the names of these functions is eabbSinglyCensored for singly censored data and eabbMultiplyCensored for multiply censored data. All of these functions are listed under the heading Estimating Distribution Parameters in the help file Censored Data. Table 1a. Available Distributions: Name, Abbreviation, Type, and Range llll{ Name Abbreviation Type Range Beta beta Continuous $[0, 1]$ Binomial binom Finite $[0, size]$ Discrete (integer) Cauchy cauchy Continuous $(-\infty, \infty)$ Chi chi Continuous $[0, \infty)$ Chi-square chisq Continuous $[0, \infty)$ Exponential exp Continuous $[0, \infty)$ Extreme evd Continuous $(-\infty, \infty)$ Value F f Continuous $[0, \infty)$ Gamma gamma Continuous $[0, \infty)$ Gamma gammaAlt Continuous $[0, \infty)$ (Alternative) Generalized gevd Continuous $(-\infty, \infty)$ Extreme for $shape = 0$ Value $(-\infty, location + \frac{scale}{shape}]$ for $shape > 0$ $[location + \frac{scale}{shape}, \infty)$ for $shape < 0$ Geometric geom Discrete $[0, \infty)$ (integer) Hypergeometric hyper Finite $[0, min(k,m)]$ Discrete (integer) Logistic logis Continuous $(-\infty, \infty)$ Lognormal lnorm Continuous $[0, \infty)$ Lognormal lnormAlt Continuous $[0, \infty)$ (Alternative) Lognormal lnormMix Continuous $[0, \infty)$ Mixture Lognormal lnormMixAlt Continuous $[0, \infty)$ Mixture (Alternative) Three- lnorm3 Continuous $[threshold, \infty)$ Parameter Lognormal Truncated lnormTrunc Continuous $[min, max]$ Lognormal Truncated lnormTruncAlt Continuous $[min, max]$ Lognormal (Alternative) Negative nbinom Discrete $[0, \infty)$ Binomial (integer) Normal norm Continuous $(-\infty, \infty)$ Normal normMix Continuous $(-\infty, \infty)$ Mixture Truncated normTrunc Continuous $[min, max]$ Normal Pareto pareto Continuous $[location, \infty)$ Poisson pois Discrete $[0, \infty)$ (integer) Student's t t Continuous $(-\infty, \infty)$ Triangular tri Continuous $[min, max]$ Uniform unif Continuous $[min, max]$ Weibull weibull Continuous $[0, \infty)$ Wilcoxon wilcox Finite $[0, m n]$ Rank Sum Discrete (integer) Zero-Modified zmlnorm Mixed $[0, \infty)$ Lognormal (Delta) Zero-Modified zmlnormAlt Mixed $[0, \infty)$ Lognormal (Delta) (Alternative) Zero-Modified zmnorm Mixed $(-\infty, \infty)$ Normal } Table 1b. Available Distributions: Name, Parameters, Parameter Default Values, Parameter Ranges, Estimation Method(s) lllll{ Default Parameter Estimation Name Parameter(s) Value(s) Range(s) Method(s) Beta shape1 $(0, \infty)$ mle, mme, mmue shape2 $(0, \infty)$ ncp 0 $(0, \infty)$ Binomial size $[0, \infty)$ mle/mme/mvue prob $[0, 1]$ Cauchy location 0 $(-\infty, \infty)$ scale 1 $(0, \infty)$ Chi df $(0, \infty)$ Chi-square df $(0, \infty)$ ncp 0 $(-\infty, \infty)$ Exponential rate 1 $(0, \infty)$ mle/mme Extreme location 0 $(-\infty, \infty)$ mle, mme, mmue, pwme Value scale 1 $(0, \infty)$ F df1 $(0, \infty)$ df2 $(0, \infty)$ ncp 0 $(0, \infty)$ Gamma shape $(0, \infty)$ mle, bcmle, mme, mmue scale 1 $(0, \infty)$ Gamma mean $(0, \infty)$ mle, bcmle, mme, mmue (Alternative) cv 1 $(0, \infty)$ Generalized location 0 $(-\infty, \infty)$ mle, pwme, tsoe Extreme scale 1 $(0, \infty)$ Value shape 0 $(-\infty, \infty)$ Geometric prob $(0, 1)$ mle/mme, mvue Hypergeometric m $[0, \infty)$ mle, mvue n $[0, \infty)$ k $[1, m+n]$ Logistic location 0 $(-\infty, \infty)$ mle, mme, mmue scale 1 $(0, \infty)$ Lognormal meanlog 0 $(-\infty, \infty)$ mle/mme, mvue sdlog 1 $(0, \infty)$ Lognormal mean exp(1/2) $(0, \infty)$ mle, mme, mmue, (Alternative) cv sqrt(exp(1)-1) $(0, \infty)$ mvue, qmle Lognormal meanlog1 0 $(-\infty, \infty)$ Mixture sdlog1 1 $(0, \infty)$ meanlog2 0 $(-\infty, \infty)$ sdlog2 1 $(0, \infty)$ p.mix 0.5 $[0, 1]$ Lognormal mean1 exp(1/2) $(0, \infty)$ Mixture cv1 sqrt(exp(1)-1) $(0, \infty)$ (Alternative) mean2 exp(1/2) $(0, \infty)$ cv2 sqrt(exp(1)-1) $(0, \infty)$ p.mix 0.5 $[0, 1]$ Three- meanlog 0 $(-\infty, \infty)$ lmle, mme, Parameter sdlog 1 $(0, \infty)$ mmue, mmme, Lognormal threshold 0 $(-\infty, \infty)$ royston.skew, zero.skew Truncated meanlog 0 $(-\infty, \infty)$ Lognormal sdlog 1 $(0, \infty)$ min 0 $[0, max)$ max Inf $(min, \infty)$ Truncated mean exp(1/2) $(0, \infty)$ Lognormal cv sqrt(exp(1)-1) $(0, \infty)$ (Alternative) min 0 $[0, max)$ max Inf $(min, \infty)$ Negative size $[1, \infty)$ mle/mme, mvue Binomial prob $(0, 1]$ mu $(0, \infty)$ Normal mean 0 $(-\infty, \infty)$ mle/mme, mvue sd 1 $(0, \infty)$ Normal mean1 0 $(-\infty, \infty)$ Mixture sd1 1 $(0, \infty)$ mean2 0 $(-\infty, \infty)$ sd2 1 $(0, \infty)$ p.mix 0.5 $[0, 1]$ Truncated mean 0 $(-\infty, \infty)$ Normal sd 1 $(0, \infty)$ min -Inf $(-\infty, max)$ max Inf $(min, \infty)$ Pareto location $(0, \infty)$ lse, mle shape 1 $(0, \infty)$ Poisson lambda $(0, \infty)$ mle/mme/mvue Student's t df $(0, \infty)$ ncp 0 $(-\infty, \infty)$ Triangular min 0 $(-\infty, max)$ max 1 $(min, \infty)$ mode 0.5 $(min, max)$ Uniform min 0 $(-\infty, max)$ mle, mme, mmue max 1 $(min, \infty)$ Weibull shape $(0, \infty)$ mle, mme, mmue scale 1 $(0, \infty)$ Wilcoxon m $[1, \infty)$ Rank Sum n $[1, \infty)$ Zero-Modified meanlog 0 $(-\infty, \infty)$ mvue Lognormal sdlog 1 $(0, \infty)$ (Delta) p.zero 0.5 $[0, 1]$ Zero-Modified mean exp(1/2) $(0, \infty)$ mvue Lognormal cv sqrt(exp(1)-1) $(0, \infty)$ (Delta) p.zero 0.5 $[0, 1]$ (Alternative) Zero-Modified mean 0 $(-\infty, \infty)$ mvue Normal sd 1 $(0, \infty)$ p.zero 0.5 $[0, 1]$ }

References

Millard, S.P. (2013). EnvStats: An R Package for Environmental Statistics. Springer, New York.