ABSTRACT:The generalized extreme value distribution is generally used to model annual maximum daily precipitation, and it then allows the calculation of the return values of this phenomenon. The distribution was fitted for selected stations in the north of Algeria; it was found that the generalized extreme value distribution of type I or the Gumbel distribution is more suitable for the Algiers and Miliana stations and the Fréchet distribution is more appropriate for the Oran station. The parameters were estimated using the maximum likelihood method, and the return levels were calculated at selected return periods T; for instance, about 100 years must elapse to record a level of 181.9 mm of rainfall per day in Algiers, 173 mm in Miliana and 109.54 mm in Oran.

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing, which makes standard lifetime models inadequate. Finite mixture models provide more flexibility for modeling such data. In this paper, the Weibull‐log‐logistic mixture distributions model is introduced as a new class of flexible models for heterogeneous lifetime data. Some statistical properties of the model are presented including the failure rate function, moments generating function, and characteristic function. The identifiability property of the class of all finite mixtures of Weibull‐log‐logistic distributions is proved. The maximum likelihood estimation (MLE) of model parameters under the Type I and Type II censoring schemes is derived. Some numerical illustrations are performed to study the behavior of the obtained estimators. The model is applied to the hard drive failure data made by the Backblaze data center, where it is found that the proposed model provides more flexibility than the univariate life distributions (Weibull, Exponential, logistic, log‐logistic, Frechet). The failure rate of hard disk drives (HDDs) is obtained based on MLE estimates. The analysis of the failure rate function on the basis of SMART attributes shows that the failure of HDDs can have different causes and mechanisms.

There are no studies and only limited data that compare the difference in mortality between twins and singletons in the Arab world. We studied the survival of 306,966 children, including 9,280 twins, over the period 1970–2013 in six Arab countries (Algeria, Egypt, Iraq, Mauritania, Sudan and Tunisia) based on the Multiple Indicator Cluster Survey (MICS) database. With the use of relative survival models, we estimated the mortality of twins relative to singletons by including socioeconomic and demographic variables. This study confirms the results of previous studies on the excess risk of death of twins compared to singletons. There is evidence that excess mortality decreases with follow-up; in addition, male twins have a higher risk of death compared to females for all countries except Tunisia. Wealth index and education levels of women are factors that influence the risk of mortality. It is recommended that these findings are considered when performing future health and population strategies in these Arab countries.

The determination of the number and the lengths of intervals of the baseline risk function λ 0 (t), is an important issue in Piecewise constant Exponential Models (PEM) and Proportional Hazard Models (PH), especially, when using Bayesian inference. In this context, we propose a simple method to estimate that number and thoses lenghts of interval for constructing Bayesian PH Cox model. Based on real data, the obtained results that the estimated parameters are not affected, but the log-likelihood and information criterion are very sensitive. On this, the problem of model selection is considered to assess the influence on decision making.

No abstract