The Generalized Odd Linear Exponential Family of Distributions with Applications to Reliability Theory

A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile functio...

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Bibliographic Details
Published in:Mathematical and computational applications 2022-08, Vol.27 (4), p.55
Main Authors: Jamal, Farrukh, Handique, Laba, Ahmed, Abdul Hadi N., Khan, Sadaf, Shafiq, Shakaiba, Marzouk, Waleed
Format: Article
Language:English
Subjects:
Asymptotes
Asymptotic properties
Distribution functions
generalized odd linear distribution
Generators
hazard rate function
Maximum likelihood estimates
Maximum likelihood estimation
moments
Monte Carlo simulation
Random variables
residual analysis
Statistical analysis
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Summary:A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile function, moment generating function, distribution of order statistics, moments, mean deviations, asymptotes and the stress–strength model of the proposed family are investigated. The maximum likelihood estimation of the parameters is presented. Simulation is carried out for two of the mentioned sub-models to check the asymptotic behavior of the maximum likelihood estimates. Two real-life data sets are used to establish the credibility of the proposed model. This is achieved by conducting data fitting of two of its sub-models and then comparing the results with suitable competitive lifetime models to generate conclusive evidence.
ISSN:2297-8747
1300-686X
2297-8747
DOI:10.3390/mca27040055