Résumé: This study introduces and examines a new probability distribution, presenting various characterizations. Key financial risk measures, including the value-at-risk (VaR), tail-value-at-risk (TVaR), also referred to as conditional tail expectation or conditional value-at-risk (CVaR), tail variance (TV), tail mean-variance (TMV), and mean excess loss (MExL) function are evaluated using maximum likelihood estimation, ordinary least squares, weighted least squares, and the Anderson-Darling estimation methods. These methods are applied for actuarial analysis in both a simulation study and an insurance claims data application. For validation of the distribution using complete data, the widely recognized Nikulin-Rao-Robson statistic is utilized and assessed through simulations and three real data sets. Two uncensored real-life data sets for failure times and remission times are used in uncensored validation. Additionally, for censored data validation, a modified version of the Nikulin-Rao-Robson statistic is proposed and evaluated through extensive simulations and three censored real data sets.

Résumé: We propose a new generator which has been used as a generalized class, and can also be helpful in generating new flexible generalized classes of distributions for continuous random variable. The newly proposed generator-cum-generalized class does not involve any extra parameter, and its functional form plays an important role along with baseline models to develop flexible models. In literature, such classes had been reported as Marshall-Olkin G-class, exponentiated G-class, Transmuted G-class, exponentiated generalized G-class, and Flexible G-class. So, any parent (or baseline) model can be substituted in the proposed class which has no extra burden on the parameters of the class. Some needful characteristics of the newly proposed class are obtained. Furthermore, a special model of the class, that is, the flexible Kumaraswamy distribution is considered and its properties are reported. The parameters estimation is dealt through the method of maximum likelihood, and a simulation is carried out to assess the performance of model’s parameters. Four real-life data sets are analyzed to show usefulness of the proposed model in comparison to some well-established competitive models. It is found that the proposed model yields low values of the goodness-of-fit statistics as compared to the other models, and hence our proposed model performed better as compared to others on these four data sets.

Résumé: A univariate generalized family of continuous distributions, tentatively called the odd moment exponential-G Poisson family of distribution, has been introduced in this article. Among various techniques, the framework of compounding has been employed to devise the odd moment exponential-G distribution with the truncated Poisson distribution. With exponential distribution as a key model of the new family, the resultant model has been studied in lieu with theoretical and applied way. The theoretical foundation has been set up including definite mathematical expressions for shapes of density and hazard function, moments and related generating functions, process of residual life and its regeneration, ordered statistics, mechanics of material expressed in stress-strength expressions, Rnyi entropy and mean deviation among others. The estimation of the model parameters is performed by the maximum likelihood method for complete and censored scenario. A simulation study (for un-censored and censored case) is carried out under varying sample sizes to assess the efficacy of the model parameters. Three applications to the failure time data sets related to system reliability are used to showcase the extensibility of the proposed family. The postulated distribution is anticipated to be adaptable enough to model data sets in circumstances where both entire (un-censored) and partial information (censored) is accessible.

Résumé: In this paper, a new family of lifetime distributions called new two-parameter distribution-G family is introduced. This family includes some new distributions such as new two-parameter distribution -generalized linear exponential family. Some statistical properties of the proposed distribution are obtained, such as the hazard rate function, moments, moment generating function and order statistics. We discuss the estimation of the distribution parameters by method of maximum likelihood in both of complete and right censored cases. A modified criteria test is developed to fit this new model when the parameters are unknown and data are right censored. The performances of the methods used are demonstrated by an intensive simulation study whether the usefulness and the versatility in practical applications of this distribution is illustrated by means of real data sets.

Résumé: In this work, we introduce a new chi-squared type test the odd Lindley exponentiated gamma distribution. The new test is an extension of the Nikulin-Rao-Robson test. The new test is tailored to fit the right censored data. The performance of the new test, as well as the baseline Nikulin-Rao-Robson test, are evaluated via numerical simulation. The new test, as well as the baseline Nikulin-Rao-Robson test, are also evaluated using the data. Furthermore, we presented some characterization results.

Résumé: In this paper we propose a new three-parameter flexible Weibull-logistic (FW-L) distribution to increase the level of flexibility of logistic distribution without increasing the number of parameters. We obtain some of fundamental mathematical properties including asymptotes, moments, quantile function, entropy, and order statistics. The goodness-of-fit test for the proposed distribution is also studied. Then, we derived estimation of model parameters for both complete and right censored data sets. Further, a simulation study is conducted to observe the asymptotic behavior of maximum likehood estimations. The flexibility and importance of the proposed models are illustrated by means of the real data set. The results of the study shows that the main advantage of the new distribution is that it has increasing, decreasing or bathtub curve failure rate depending upon the shape parameter. This property makes FW-L is very useful in data analysis.

Résumé: A modified version of Bagdonavičius-Nikulin goodness-of-fit statistical test is presented for validation under the right censor case. Simulation via Barzilai-Borwein algorithm is performed for assessing the right-censorship estimation method. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

Résumé: Al-Shomrani et al. (2016) introduced a new family of distributions (TL-G) based on the Topp-Leone distribution (TL) by replacing the variable x by any cumulative distribution function G(t). With only one extra parameter which controls the skewness, this family is a good competitor to several generalized distributions used in statistical analysis. In this work, we consider the extended exponential as the baseline distribution G to obtain a new model called the Topp-Leone extended exponential distribution TL-EE. After studying mathematical and statistical properties of this model, we propose different estimation methods such as maximum likelihood estimation, method of ordinary and weighted least squares, method of percentile, method of maximum product of spacing, method of Cramer Von-Mises, modified least squares estimators and chi-square minimum method for estimating the unknown parameters. In addition to the classical criteria for model selection, we develop for this distribution a goodness-of-fit statistic test based on a modification of Pearson statistic. The performances of the methods used are demonstrated by an extensive simulation study. With applications to covid-19 data and waiting times for bank service, a comparison evaluation shows that the proposed model describes data better than several competing distributions.

Résumé: The Poisson Topp Leone Burr XII distribution is studied mainly for illustrating its wide applicability under censored (engineering, economic and medical) real data sets. Four real data sets are analyzed, the Poisson Topp Leone Burr XII distribution is compared with nine Burr type XII extensions which provided the best fits. A modified Bagdonavičius-Nikulin goodness-of-fit test statistic is presented and applied for distributional validation under the right censor case for the Poisson Topp Leone Burr XII distribution. The four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation. The Barzilai-Borwein algorithm is used for assessing the modified Bagdonavičius-Nikulin goodness-of-fit test statistic using a simulation study.

Résumé: In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets.