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

Abstract

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

“…We shall compare thefits of the OBEE distribution with those of other competitive models [43] and Al-Babtain et al [3]. For comparing models, we consider the Cramér-Von Mises (C • ) and the Anderson-Darling (A • ) and the Kolmogorov-Smirnov (KS) statistic.…”

“…The first data set {1.1, 0.7, 1.9, 3.0, 1.7, 1.0, 1.8, 1.5, 1.2, 1.8, 1.6, 2.7, 4.1, 1.4, 1.3, 1.7, 2.2, 1.4, 2.3, 1.6, 2} called the failure time data: The data represents the lifetime data relating to relief times (in minutes) of patients receiving an analgesic (see Gross and Clark [30]). This data was recently analyzed by Ibrahim et al [40] and Al-Babtain et al [3]. Table 2 lists the MLEs, StErs confidence intervals (CIs).…”

New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling

“…This data are given in Appendix(d).These data have also been analyzed by Smith and Naylor [51].For this data set,we shall compare the fits of the new distribution with some competitive models like OLEW,E-W,T-W.Based on the Table 9 we conclude that the proposed MOL-W model is the best model with CV M statistic = 0.10565 and AD statistic = 0.59106. Many other useful version can be used in more comparisons see Al-Babtain et al [1],Al-Babtain et al [2],Ibrahim et al [24],Ibrahim and Yousof [25], Ibrahim and Yousof [26]Ibrahim et al [27], Alshkaki [6]and Esmaeili et al [16]. The HRF of the MOL-W distribution exhibits "constant hazard rate (α = 1, β=1, a 1 = 1, a 2 = 1)", "upside down-constant (α = 0.5, β=0.5, a 1 = 1.01, a 2 = 1)", "decreasing hazard rate (α = 0.5, β=5, a 1 = 1, a 2 = 0.2)", "increasing-constant hazard rate (α = 0.5, β=0.15, a 1 = 1.25, a 2 = 1)", "increasing hazard rate (α = 2, β=1, a 1 = 1.5, a 2 = 1)", "J-hazard rate (α = 0.5, β=1, a 1 = 20, a 2 = 1)" and "decreasing hazard rate (α = 0.2, β=1, a 1 = 0.1, a 2 = 1)".…”

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.…”