The generalized odd Burr III family of distributions: properties, applications and characterizations

Classical and Bayesian inference for the new four-parameter Lomax distribution with applications

In this study, a new four-parameter Lomax distribution is proposed using a new alpha power transformation technique. The new distribution is named "New Alpha Power Transformed Power Lomax Distribution." Mathematical properties, including moments, the moment-generating function, the mean residual life, order statistics, and the quantile function, are obtained. The maximum likelihood estimation approach is used to estimate the model parameters. A comprehensive simulation is used to evaluate the behavior of maximum likelihood estimators. Two real-world data sets were used to demonstrate the significance of the proposed model, and the results show that the new model performs better when interpreting lifetime data sets. In the end, for the data sets, Bayesian estimation and Metropolis-Hasting's approach were also utilized to construct the approximate Bayes estimates, and convergence diagnostic methods based on Markov Chain Monte Carlo techniques were applied.

Control chart for half normal and half exponential power distributed process

In this manuscript, we construct an attribute control chart (ACC) for the number of defective items using time-truncated life tests (TTLT) when the lifetime of a manufacturing item follows two lifetime data distributions: the half-normal distribution (HND) and the half-exponential power distribution (HEPD). To assess the potential of the proposed charts, necessary derivations are made to obtain the value of the average run length (ARL) when the production process is in-control and out-of-control. The performance of the presented charts is evaluated for different sample sizes, control coefficients, and truncated constants for shifted phases in terms of ARL. The behavior of ARLs is studied for the shifted process by introducing shifts in its parameters. The advantages of the proposed HEPD-based chart are discussed in the form of ARLs with HND and Exponential Distribution (ED) based ACCs under TTLT, showing the excellent assessment of the proposed chart. Additionally, the advantages of another proposed ACC using HND are compared with ED-based ACC, and the findings support the HND in the form of smaller ARLs. Finally, simulation testing and real-life implementation are also discussed for functional purposes.

On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications

In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.