A new class of distributions based on the zero truncated Poisson distribution with properties and applications

Abstract

We study a new family of distributions defined by the minimum of the Poisson random number of independent and identically distributed random variables having the Topp Leone-G distribution. Some mathematical properties of the new family are derived. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of the proposed family. In order to test the validity of the new family, a modified Chi-squared goodness-of-fit test based on Nikulin-Rao-Robson statistics is proposed theoretically.

WITHDRAWN: The Generalized Weibull Poisson G Family of Continuous Probability Distributions with Copulas, Mathematical Properties and Applications to Real Data Sets

“…where the function 𝓤 𝒸,𝓥 (𝓌) = [𝓗 𝓥 (𝓌)/𝓗 𝓥 (𝓌)] 𝒸 | 𝓌∈𝓡 , refers to the function if the odd ration function (ORF), 𝓗 𝓥 (𝓌) refers to the CDF of the baseline model with parameters vector 𝓥, 𝓗 𝓥 (𝓌) refers to the survival function (SF) base line model, 𝑑𝓗 𝓥 (𝓌)/𝑑𝓌 =𝓱 𝓥 (𝓌) is the base line PDF and 𝒷, 𝒸 > 0 is a shape parameters. Starting from (1) and for 𝒸 = 2, the GW-G family become the generalized-Rayleigh G (RR-G) (see Yousof et al (2017a)). Let the RV 𝒴 𝓅 denote the failure time of the i th subsystem and let 𝑊 = 𝓂𝑖𝑛{𝒴 1 , 𝒴 2 , ⋯ , 𝒴 𝑁 }.…”

A New Probability Distribution for Modeling Failure and Service Times: Properties, Copulas and Various Estimation Methods

“…So, we used it in comparing competitive models. Before using the the maximum likelihood method, we performed simulation experiments to assess the finite sample behavior of it using the biases and mean squared errors As a future potential work we may consider the modified Nikulin-Rao-Robson goodness-of-fit test for distributional validation as presented by Abouelmagd et al [1], Abouelmagd et al [2], Ibrahim et al [39], brahim et al [37], Goual et al [28] and Goual et al [29]. We may consider the modified Bagdonavičius-Nikulin Goodnessof-fit test for censored validation as presented by Mansour et al ([53], [54], [56], [57], [52] and [55]), Yousof et al [67] and Salah et al [61].…”

The Extended Exponential Weibull Distribution: Properties, Inference, and Applications to Real‐Life Data

“…Additional important generalized forms of the Weibull model are introduced by Korkmaz et al [22][23][24], Abouelmagd et al [25][26][27], Cordeiro et al [28], Bhatti et al [29], Nasir et al [30], Alizadeh et al [31], Afify et al [32,33], Hussein et al [34], Mead et al [35] and Nassar et al [36].…”