Abstract
The recent exponentiated generalized linear exponential distribution is a generalization of the generalized linear exponential distribution and the exponentiated generalized linear exponential distribution. In this paper, we study some statistical properties of this distribution such as negative moments, moments of order statistics, mean residual lifetime, and their asymptotic distributions for sample extreme order statistics. Different estimation procedures include the maximum likelihood estimation, the corrected maximum likelihood estimation, the modified maximum likelihood estimation, the maximum product of spacing estimation, and the least squares estimation are compared via a Monte Carlo simulation study in terms of their biases, mean squared errors, and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate its use for modeling a rainfall data from Orlando, Florida.
Highlights
When β = 1, the distribution is reduced to the generalized linear exponential distribution (GLED) (Mahmoud and Alam [2]), and when λ3 = 0, it reduced to the exponentiated generalized linear exponential distribution (EGLED)
We study some statistical properties of this distribution such as negative moments, moments of order statistics, mean residual lifetime, and their asymptotic distributions for sample extreme order statistics
Let X1, . . . , Xn be a random sample from the new exponentiated generalized linear exponential distribution (NEGLED)(λ1, λ2, λ3, α, β)
Summary
Poonia and Azad [1] studied a new exponentiated generalized linear exponential distribution (NEGLED) with cumulative distribution density function (CDF). Poonia and Azad [1] have shown in the graphs that the distribution has decreasing, decreasing-increasing type, right-skewed, unimodal or bimodal probability density function (PDF) and increasing, decreasing or bathtub shaped hazard rate They discussed the statistical properties such as moments, quantiles, order statistics, hazard rate function (HRF), stress–strength parameter, and investigated the estimation of the parameters using the maximum likelihood estimation (MLE) method. For some distributions in which the origin is unknown, such as the lognormal, gamma, and Weibull distributions, maximum likelihood estimation can break down This difficulty can arise in the case of the GLED or NEGLED and has not been addressed in the work of Mahmoud and Alam [2] and Poonia and Azad [1].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
