A new method for generating distributions with an application to exponential distribution

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in detail, namely one-parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the momen...

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Veröffentlicht in:Communications in statistics. Theory and methods Jg. 46; H. 13; S. 6543 - 6557
Hauptverfasser: Mahdavi, Abbas, Kundu, Debasis
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Taylor & Francis 03.07.2017
Taylor & Francis Ltd
Schlagworte:
Economic models
Entropy
Exponential distribution
Fisher information matrix
Flexibility
Formulas (mathematics)
Hazard rate function
Mathematical models
Maximum likelihood estimation
Parameters
Primary: 62E15
Probability distribution functions
Quantiles
Secondary: 62H10
Statistics
Survival function
ISSN:0361-0926, 1532-415X
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Beschreibung
Zusammenfassung:A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in detail, namely one-parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment-generating function, mean residual lifetime, stochastic orders, order statistics, and expression of the entropies, are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non linear equations only. Further, we consider an extension of the two-parameter exponential distribution also, mainly for data analysis purposes. Two datasets have been analyzed to show how the proposed models work in practice.
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ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2015.1130839