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K-distribution
About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.
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09 Sep 2022
TL;DR: In this paper , the authors describe the probability distributions in R and demonstrate the central limit theorem using R's functions to generate data from a specific distribution, and demonstrate how to generate random numbers from the distribution.
Abstract: This chapter describes the probability distributions in R. Probability distributions are categorised as being either discrete or continuous, though it is possible to have a distribution with both elements. Discrete and continuous distributions are characterised by mathematical functions. The chapter starts with the idea of independent events, before considering independent random variables. R has a wide range of built-in probability distributions. For each of R's supported distributions, four functions are available that complete certain tasks: the probability density function, the cumulative probability, the quantiles of the distribution, and random numbers generated from the distribution. The chapter demonstrates the central limit theorem using R's functions to generate data from a specific distribution.
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TL;DR: In this article, four new probability models are derived which generalize the common univariate continuous distributions, including probability density function, moments generating function, cumulative distribution function, derivatives, inverse distributions, skewness, kurtosis, change of variable distributions.
Abstract: Four new probability models are derived which generalize the common univariate continuous distributions. Classical distributional measures are derived from Hoel, et al., Introduction to Probability Theory, 1971. Measures include probability density function, moments generating function, cumulative distribution function,derivatives, inverse distributions, skewness, kurtosis, change of variable distributions, log distributions. Maximum likelihood estimation technique is briefly outlined. Appendices describe applications. Errata/addenda sheet included.