Abstract
The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood (), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramér–von Mises statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.
Highlights
Erlang-Truncated Exponential (ETE) distribution was originally introduced by El-Alosey [1] as an extension of the standard one parameter exponential distribution
We shall investigate the stability of the mle estimates of the parameters of the Extended Erlang-Truncated Exponential (EETE) distribution with different sample size (n) through a Monte-Carlo study, followed by a real-life example of possible application of the new distribution
The simulation procedure as outlined below was performed in R (Statistical software): 1. simulate a random sample of size n from the EETE distribution with parameters α = 5, β = 5 and λ = 5 using the inversion of the cdf method with Equation (11)
Summary
Article No~e00296Erlang-Truncated Exponential (ETE) distribution was originally introduced by El-Alosey [1] as an extension of the standard one parameter exponential distribution. The ETE distribution share the same limitation of constant failure rate property with the exponential distribution which makes it unsuitable for modelling many complex lifetime data sets that have nonconstant failure rate characteristics. Research has shown that the standard probability distributions are largely inadequate for modelling complex lifetime data sets and various excellent ways of overcoming this shortcoming have been proposed in the literature; for instance: Beta exponential G distributions, due to Alzaatreh et al [2]; Beta extended G distributions, due to Cordeiro et al [3]; Beta G distributions, due to Eugene et al [4]; Exponentiated exponential Poisson G distributions, due to Ristić and Nadarajah [5]; Exponentiated generalized G distributions, due to Cordeiro et al [6]; Marshall–Olkin G distributions, due to Marshall and Olkin [7]; Transmuted family of distributions, due to Shaw and Buckley [8]; and so on
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