Abstract
The Marshall–Olkin Extended Exponential distribution is introduced and reliability properties are studied. The p.d.f.’s of nth record value, joint p.d.f.’s, of mth and nth record values are derived to obtain the expression for mean, variance and covariance of reord values. The entropy of jth record value is derived.The stress strength analysis for the new model is carried out. We develop autoregressive processes and sample path properties are explored. The results are verified using simulations as well as graphical studies.The model is extended to higher orders also.
Highlights
Exponential distributions play a central role in analysis of lifetime or survival data, in part because of their convenient statistical theory, their important ‘lack of memory’ property and their constant hazard rates
In circumstances where the one-parameter family of exponential distributions is not sufficiently broad, a number of wider families such as the gamma, Weibull and Gompertz-Makeham distributions are in common use; these families and their usefulness are described by various authors
We introduce the Marshall–Olkin Extended Exponential distribution MOEE(α, λ ) in section 2 and its properties are studied
Summary
Exponential distributions play a central role in analysis of lifetime or survival data, in part because of their convenient statistical theory, their important ‘lack of memory’ property and their constant hazard rates. New parameters can be introduced to expand families of distributions for added flexibility or to construct covariate models. The family of Weibull distributions contains the exponential distributions and is constructed by taking powers of exponentially distributed random variables. The family of gamma distributions contains the exponential distributions, and is constructed by taking powers of the Laplace transform. The new hazard (failure) rate function is given by r(x). We introduce the Marshall–Olkin Extended Exponential distribution MOEE(α, λ ) in section 2 and its properties are studied. The probability p is estimated and the standard error of the estimated value is calculated numerically by simulation
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