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In this work, a novel probability distribution is introduced and studied. Some characterizations are presented. Several financial risk indicators, such as the value-at-risk, tail-valueat-risk, tail variance, tail Mean-Variance, and mean excess loss function are considered under the maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson Darling estimation methods. These four methods were applied for the actuarial evaluation under a simulation study and under an application to insurance claims data. For distributional validation under the complete data, the well-known Nikulin-Rao-Robson statistic is considered. The Nikulin-Rao-Robson test statistic is assessed under a simulation study and under three complete real data sets. For censored distributional validation, a new version of the Nikulin-Rao-Robson statistic is considered. The new Nikulin-Rao-Robson test statistic is assessed under a comprehensive simulation study and under three censored real data sets. [ABSTRACT FROM AUTHOR]

In our paper, we introduce a novel extension of the Lomax distribution, aiming to enhance its applicability in various contexts. We emphasize a pragmatic approach in deriving mathematical properties of the new distribution, prioritizing its practical implications. Three distinct methods for characterizing the distribution are thoroughly discussed to provide a comprehensive understanding. The parameters of this newly proposed distribution are estimated through a diverse set of classical methodologies as well as Bayes’ method. Additionally, we develop the censored case maximum likelihood method to address scenarios where data may be incomplete. We meticulously compare the efficacy of likelihood estimation and Bayesian estimation using Pitman’s proximity criterion, thereby offering insights into their relative performance. For Bayesian estimation, we employ three distinct loss functions: the generalized quadratic, the Linex, and the entropy functions, each offering unique perspectives on the estimation process. Through extensive simulation experiments, we meticulously evaluate the performance of all estimation methods under various conditions, providing valuable insights into their practical utility. Furthermore, we conduct a comparative analysis between the Bayesian technique and the censored maximum likelihood method using the BB algorithm, facilitating a nuanced understanding of their respective strengths and weaknesses. In addition to estimation methodologies, we delve into the construction of the Nikulin-Rao-Robson statistic for the new model under both uncensored and censored cases. Detailed simulation studies and the presentation of two real-world applications elucidate the practical significance of our proposed statistics in diverse scenarios. Overall, our paper not only introduces a novel extension of the Lomax distribution but also provides a comprehensive exploration of various estimation techniques and statistical measures, underpinning its practical relevance across different domains. [ABSTRACT FROM AUTHOR]

In this paper we present a new exponential accelerated failure time model. Some of its properties and characterization results are derived. Different estimation methods are considered for assessing the finite sample behavior of the estimators. Simulation studies for comparing the estimation methods are performed. Finally, we present a novel modified chi-square test for the novel exponential accelerated failure time model in both complete and right censored data cases. The validity of the new model is checked by using the theoretical global of the Nikulin-Rao-Robson. The maximum likelihood method is considered for this purpose. Two simulation studies are performed for assessing the exponential accelerated failure time model and the efficiency of the Nikulin-RaoRobson test statistic, respectively. Three real data sets are considered for illustrating the efficiency of the test statistic in validation. [ABSTRACT FROM AUTHOR]

We provide a new extension of the exponential distribution with an emphasis on the practical elements of the model. Six different classical estimation methods were applied and compared. The main test was evaluated on complete data using four sets of data. Additionally, four applications and the derivation of the new Nikulin statistic test for the new probability model under the censored situation are described. Both tests were evaluated through simulation experiments on complete data and on artificial and censored data. In addition, a set of simulation experiments were presented, which were used and employed to evaluate the original statistical test and the new modified statistical test based on statistical controls in the evaluation processes. [ABSTRACT FROM AUTHOR]

We propose a new extension of the exponential distribution for right censored Bayesian and non-Bayesian distributional validation. The parameter of the new distribution is estimated using several conventional methods, including the Bayesian method. The likelihood estimates and the Bayesian estimates are compared using Pitman's closeness criteria. The Bayesian estimators are derived using three loss functions: the extended quadratic, the Linex, and the entropy functions. Through simulated experiments, all the estimating approaches offered have been assessed. The censored maximum likelihood method and the Bayesian approach are compared using the BB algorithm. The development of the Nikulin–Rao–Robson statistic for the new model in the uncensored situation is thoroughly discussed with the aid of two applications and a simulation exercise. For the novel model under the censored condition, two applications and the derivation of the Bagdonavičius and Nikulin statistic are also described. [ABSTRACT FROM AUTHOR]

This paper, we firstly introduce a new extension of the exponentiated exponential distribution along with sufficient set of its mathematical properties. Secondly, we construct a modified Chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic in presence of censored and complete data. We describe the theory and the mechanism of the Yn² statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored. [ABSTRACT FROM AUTHOR]