Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation

Abstract

In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal with a heavy tail with positive skewness. The new failure rate function can be “upside-down”, “decreasing” with many different shapes and “decreasing-constant”. Some mathematical and statistical properties of the new model are derived. The model parameters are estimated using different estimation methods. For comparing the estimation methods, Markov Chain Monte Carlo (MCMC) simulations are performed. The applicability of the new model is illustrated via four real data applications, these data sets are symmetric and right skewed. We constructed a modified Chi-Square goodness-of-fit test based on Nikulin-Rao-Robson test in the case of complete and censored sample for the new model. Different simulation studies are performed along applications on real data for validation propose.

A New Family of Continuous Probability Distributions

“…The goodness-of-fit (GOF) statistic called "Akaike information" (AICr), consistent-AIC (CAICr), Bayesian-IC (BICr), and Hannan-Quinn-IC (HQICr) were analyzed by comparing the competitive PII models. However, many other PII extensions could be considered in comparisons [37][38][39][40][41][42][43][44][45]. For failure times real-life data, relevant numerical results are shown in Tables 5 and 6.…”

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

“…The * and * statistics are given by: * = (1 + 1/2 ) 1/(12 ) + , and: * = ( ) + , We compared the fits of the MOBE-2 distribution with some competitive models, namely: exponential (E (β)), odd Lindley exponential (OLiE), MO exponential (MOE (α, β)), moment exponential (MomE (β)), the logarithmic Burr-Hatke exponential (Log BrHE (β)), generalized MO exponential (GMOE (α, α, β)), beta exponential (BE (a, b, β)), MO-Kumaraswamy exponential (MOKwE (α, a, b, β)), Kumaraswamy exponential (KwE (a, b, β)), and Kumaraswamy MO exponential (KwMOE (α, a, b, β)). See the PDFs of the competitive moels in [21][22][23][24][25][26][27][28][29][30][31]. We considered the Cramér-Von Mises (W * ), the Anderson-Darling (A * ), and the Kolmogorov-Smirnov (KS) statistics.…”

A Generalization of Lomax Distribution with Properties, Copula and Real Data Applications

“…The hazard rate function (HRF) for the GOLLLx model can be obtained from Yadav et al (2020). Based on generalized binomial expansions and after some algebraic processes, the PDF in (6) can be rewritten as…”