Abstract
A new three-parameter extension of the generalized Nadarajah-Haghighi model is introduced and studied. Some of its statistical properties are derived. Characterization results are presented. The failure rate can be "increasing", "decreasing", "bathtub", "upside-down", "upside-down-constant", "increasing-constant" or "constant". Different non-Bayesian estimation methods under uncensored scheme are considered. Numerical simulations are performed for comparing the estimation methods using different sample sizes. The censored Barzilai-Borwein algorithm is employed via a simulation study. Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. Based on the maximum likelihood estimators on initial data, the modified Bagdonavicius-Nikulin chi-square goodness-of-fit test recovers the loss in information. The modified Bagdonavicius-Nikulin test for validation under the right censored data is applied to four real and right censored data sets. The new model is compared with many other competitive models by means of a real data set.
Highlights
Lemonte (2013) proposed a new three-parameter model called the generalized Nadarajah-Haghighi (GNH)
Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the Burr X generalized Nadarajah-Haghighi (BXGNH) model
Characterization results based on a simple relationship between two truncated moments, in terms of the hazard rate function (HRF) and based on the conditional expectation of a function of the random variable (RV) are presented with details
Summary
Lemonte (2013) proposed a new three-parameter model called the generalized Nadarajah-Haghighi (GNH). Where a > 0 is the shape parameter, π(Φ)(z) and Π(Φ)(z) denote the PDF and CDF of the baseline model with parameter vector ξ , Πξ(z) = 1 − Πξ(z) and πξ(z) = dΠξ(z)/dz. To this end, we use Πb,θ,β(z) and equation (1). For a = θ = 1, the BXGNH distribution reduces to the Rayleigh generalized exponential (RGE) model. For θ = 1, the BXGNH distribution reduces to the BX generalized exponential (BXGE) model. The statistical literature review contains many useful Nadarajah-Haghighi extensions such as see Nascimento et al, (2019), Elsayed and Yousof (2019), Alizadeh et al, (2018) and Ibrahim (2020) for more details
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