General two-parameter distribution: Statistical properties, estimation, and application on COVID-19.

In this paper, we introduced a novel general two-parameter statistical distribution which can be presented as a mix of both exponential and gamma distributions. Some statistical properties of the general model were derived mathematically. Many estimation methods studied the estimation of the proposed model parameters. A new statistical model was presented as a particular case of the general two-parameter model, which is used to study the performance of the different estimation methods with the randomly generated data sets. Finally, the COVID-19 data set was used to show the superiority of the particular case for fitting real-world data sets over other compared well-known models.

Decision-Making for the Lifetime Performance Index.

The purpose of this research is to develop a maximum likelihood estimator (MLE) for lifetime performance index C L for the parameter of mixture Rayleigh-Half Normal distribution (RHN) under progressively type-II right-censored samples under the constraint of knowing the lower specification limit (L). Additionally, we suggest an asymptotic normal distribution for the MLE for C L in order to construct a mechanism for evaluating products' lifespan efficiency. We have specified all the steps to carry out the test. Additionally, not only does hypothesis testing successfully assess the lifetime performance of items, but it also functions as a supplier selection criterion for the consumer. Finally, we have added two real data examples as illustration examples. These two applications are provided to demonstrate how the results can be applied.

Rayleigh-half normal distribution for modeling tooth movement data.

Clear aligners provide a recent technique to induce orthodontic tooth movement. In this paper, a new one-parameter model, called, Rayleigh-Half Normal distribution (RHN) is proposed for modeling tooth movement data. Various statistical and reliability properties including moments and its associated measures, mean residual life, survival and hazard functions are derived and studied. Moreover, the model parameter is estimated via the method of moments and maximum likelihood. A simulation study was performed to examine the bias and mean square error of the estimated parameter. Finally, the flexibility of the proposed model is illustrated by utilizing a real dental data. The results showed that it could give a better fit than other well-known models.