The Generalized Transmuted Poisson-G Family of Distributions: Theory, Characterizations and Applications

Abstract

In this work, we introduce a new class of continuous distributions called the generalized poissonfamily which extends the quadratic rank transmutation map. We provide some special models for thenew family. Some of its mathematical properties including Rényi and q-entropies, order statistics andcharacterizations are derived. The estimations of the model parameters is performed by maximumlikelihood method. The Monte Carlo simulations is used for assessing the performance of the maximumlikelihood estimators. The ‡exibility of the proposed family is illustrated by means of two applicationsto real data sets.

A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

“…In this Section, two real data applications are presented for illustrating the importance and flexibility of the new model. The first data set (1.1, 1.4, 1.3, 1.7, 1.9, 1.8, 1.6, 2.2, 1.7, 2.7, 4.1, 1.8, 1.5, 1.2, 1.4, 3, 1.7, 2.3, 1.6, 2), called the failure time data, represents the lifetime data relating to relief times (in minutes) of patients receiving an analgesic (for more applications to this data see [6][7][8][9][10][11][12]).…”

A New Bimodal Distribution for Modeling Asymmetric Bimodal Heavy-Tail Real Lifetime Data

“…Here, we shall compare the fits of the OBBX distribution with those of other competitive models, namely, the BX [1], odd Lindley exponentiated W (OLEW) [24], Burr X EW (BXEW) [22], Poisson Topp Leone W (PTLW) [25], Marshall Olkin extended-W (MOEW) [26], gamma-W (GamW) [27], Kumaraswamy-W (KumW) [28], beta-W [29], transmuted modified-W (TrMW) [30], modified beta-W (MBW) [31], Mcdonald-W (MacW) [32], and transmuted exponentiated generalized W (TrEGW) [33] distributions. Some other extensions of the W distribution can also be used in this comparison, but are not limited to [34][35][36][37][38][39][40][41][42][43]. Figure 9 presents the TTT, box, Q-Q, and NKDE plots for data set I.…”

Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

“…On the other side, in the recent years, the Topp-Leone distribution reveals to be particularly efficient to define general families of distributions enjoying nice properties, including a great ability to model different practical data sets. Among these families, there are the Topp-Leone-G family studied via different approaches by [11][12][13][14], the Topp-Leone-G power series family by [15,16], the type II Topp-Leone-G family by [17], the Topp-Leone odd log-logistic family by [18], the type II generalized Topp-Leone-G family by [19], the Fréchet Topp-Leone-G family by [20], the exponentiated generalized Topp-Leone-G family by [21] and the transmuted Topp-Leone-G family by [22]. Now, for the purposes of this paper, let us describe the general family introduced by [23].…”