Generalising Exponential Distributions Using an Extended Marshall–Olkin Procedure

A new uniform distribution model, generalized powered uniform distribution ( GPUD ), which is based on incorporating the parameter k into the probability density function (pdf) associated with the power of random variable values and includes a powered mean operator, is introduced in this paper. From this new model, the shape properties of the pdf as well as the higher-order moments, the moment generating function, the model that simulates the GPUD and other important statistics can be derived. This approach allows the generalization of the distribution presented by Jayakumar and Sankaran (2016) through the new distribution. Two sets of real data related to COVID-19 and bladder cancer were tested to demonstrate the proposed model’s potential. The maximum likelihood method was used to calculate the parameter estimators by applying the maxLik package in R. The results showed that this new model is more flexible and useful than other comparable models.

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“…2020 ) and Marshall–Olkin exponentiated generalized (García et al. 2020 ) models. Finally, the conclusions are presented in Sect.…”

Section: Introductionmentioning

confidence: 99%

An extended approach for the generalized powered uniform distribution

2022

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“…A simulation study and a real world application are also worked out to assess the maximum likelihood estimators and to illustrate the theory. Garcia et al 32 presented a three-parameter family of distributions which includes the common exponential and the Marshall-Olkin exponential as special cases. This distribution shows a monotone failure rate, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these disadvantages, such as the Weibull and gamma three-parameter families.…”

Section: Introductionmentioning

confidence: 99%

A review on recent generalizations of exponential distribution

Tomy¹,

Jose²,

Veena³

2020

BBIJ

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Kondo 1 as Pearson's type X distribution when the sampling of standard deviation was discussed.These distributions have been widely used to analyze lifetime data, on account of its analytical tractability, also used in physics, queueing theory, and hydrology, often used to model the reliability of electronic systems, which do not typically experience wear-out type failures. Exponential variables can also be used to model situations where certain events occur with a constant probability per unit length, such as the distance between mutations on a DNA strand, or between road kills on a given road.

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