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Full-Text Articles in Probability
Distribution Of A Sum Of Random Variables When The Sample Size Is A Poisson Distribution, Mark Pfister
Distribution Of A Sum Of Random Variables When The Sample Size Is A Poisson Distribution, Mark Pfister
Electronic Theses and Dissertations
A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when the sample size …
Some New And Generalized Distributions Via Exponentiation, Gamma And Marshall-Olkin Generators With Applications, Hameed Abiodun Jimoh
Some New And Generalized Distributions Via Exponentiation, Gamma And Marshall-Olkin Generators With Applications, Hameed Abiodun Jimoh
Electronic Theses and Dissertations
Three new generalized distributions developed via completing risk, gamma generator, Marshall-Olkin generator and exponentiation techniques are proposed and studied. Structural properties including quantile functions, hazard rate functions, moment, conditional moments, mean deviations, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates are presented. Monte Carlo simulation is employed to examine the performance of the proposed distributions. Applications of the generalized distributions to real lifetime data are presented to illustrate the usefulness of the models.