Study on an Extension to Lindley Distribution: Statistical Properties, Estimation and Simulation

Abstract

Recently, Nedjar and Zeghdoudi [6] proposed a new lifetime model called gamma Lindley distribution. Roozegar and Nadarajah [8] introduced some notes around gamma Lindley distribution including only some statistical properties and estimations depending on the same probability density function which proposed by Nedjar and Zeghdoudi [6]. In fact, the model proposed by Nedjar and Zeghdoudi [6] is not a probabilistic model. Further, some of its fundamental properties as well as parameter estimations are incorrect. Hence, all corrections which proposed by Roozegar and Nadarajah [8] are also incorrect. On the other hand, Messaadia and Zeghdoudi [5] proposed only one remark around the parameter space of gamma Lindley distribution which proposed by Nedjar and Zeghdoudi [6], but the mathematical properties and estimations are still wrong for both Nedjar and Zeghdoudi [6] and Roozegar and Nadarajah [8]. Because, Messaadia and Zeghdoudi [5] did not discuss any corrections around quantile function, entropies, estimation methods, simulation and data analysis. In this paper, several corrections including probability density function, quantile function, entropies, estimation the model parameters using the maximum likelihood estimation and moment estimation methods and simulation are discussed in-detail because the previous three papers not make a benefit to the readers, especially in practical field.

On the Extension of the Burr XII Distribution: Applications and Regression

“…Also, using the GenSA package in R, the initial values of the parameters of the fitted models used for the optimisation are obtained. The performance of the HMBXII distribution is compared with nine (9) modifications of the Burr XII distribution which include the Marshall-Olkin exponentiated Burr XII distribution (MOEBXII) [2], the exponentiated Burr XII Poisson distribution (EBXIIP) [22], the Marshall-Olkin generalised Burr XII distribution (MOGBXII) [3], the Weibull Burr XII distribution (WBXII) [6], the Kumaraswamy exponentiated Burr XII distribution (KEBXII) [5], the Kumaraswamy Burr XII distribution (KWBXII) [7], the study on an extension to Lindley distribution [9] the exponentiated Exponential Burr XII distribution (EEBXII) [10], the Gompertz-modified Burr XII distribution (GMBXII) [13] and the odd exponentiated half-logistic Burr XII distribution (OEHLBXII) [14]. The Kolmogorov-Smirnov(K-S), Anderson-Darling(AD) and Cramér-von Mises (CVM) tests were used to evaluate the goodness-of-fit of the distributions fitted to the data.…”

Statistical modelling for the Covid-19 mortality rate in the Kingdom of Saudi Arabia

“…These computations were carried out using the software. Many papers used optimization methods as [23] , [24] , [25] , [26] .…”

Exponentiated Generalized Weibull Exponential Distribution: Properties, Estimation and Applications

“…They estimated the model parameters via several methods namely; maximum likelihood, maximum product of spacing, and Bayesian. For more recently papers see [17,18]. Moreover, Bilal et al [19] introduced a new Weibull class of distributions with CDF and PDF given by Equation (1.3) and Equation (1.4)…”