Résumé: In this work, we introduce a new lifetime distribution called the Square Lindley Pareto (SLP) distribution and explore its fundamental properties. Particular attention is given to the cumulative distribution function, as well as the monotonic behavior of the probability density and hazard rate functions. Wealso derive expressions for the moment-generating function, moments (including mean and variance), stress-strength reliability, mean deviations, Rényi and Shannon entropy, the quantile function, and extreme order statistics. Furthermore, a comprehensive simulation study is conducted to evaluate the performance of five parameter estimation methods: maximum likelihood estimation (MLE), Anderson–Darling, Cramér–von Mises, maximum product of spacings, and least squares. The estimators are compared based on average absolute bias, mean squared error, and mean absolute relative error. To illustrate the flexibility and practical applicability of the proposed distribution, we analyze four different real-world data sets. The results confirm the SLP distribution’s strong modeling capability and its usefulness in various applied f ields such as reliability and survival analysis.

Résumé: In this paper, we introduce a new lifetime distribution called alpha power one-parameter Weibull (APOPW) distribution based on the alpha power transformation method has been defined and studied. Various statistical properties of the newly proposed distribution including moments, moment generating function, quantile function, R´ enyi and Shannon entropy, stress-strength reliability, mean deviations, and extreme order statistics have been obtained. Several estimation techniques are studied, including maximum likelihood estimation (MLE), Anderson–Darling (AD), least squares estimation (LSE), Cram´er–von Mises (CVM), and maximum product of spacings (MPS). The estimators compared their efficiency based on average absolute bias (BIAS), mean squared error (MSE), and mean absolute relative error (MRE), identifying that MLE as the most robust method across various sample sizes increase. The efficiency and flexibility of the new distribution are illustrated by analysing two real-live data sets, and compare its goodness-of-fit against several existing lifetime distributions.

Résumé: We show that the integration by parts formula based on Malliavin-Skorohod calculus techniquesfor additive processes helps us to compute quantities like E(LTh(LT)),or more generally E(H(LT)),fordifferent suitable functionshorHand different models for the cumulative loss processL.These quantities areimportant in Insurance and Finance. For example they appearin computing expected shortfall risk measuresor prices of stop-loss contracts. The formulas given in the present paper generalize the formulas given in arecent paper by Hillairet, Jiao and R ́eveillac (HJR). In theHJR paper, despite the use of advanced models,including the Cox process, the treatment of the formulas is based only on Malliavin calculus techniques forthe standard Poisson process, a particular case of additiveprocess. In the present paper, Malliavin calculustechniques for additive processes are used, more general results are obtained and proofs appears to be shorter.

Résumé: Managing and controlling risk is a topic research in the world of finance. Before a risky situation, the stakeholders need to do comparison according to the positions and actions, and financial institutions must take measures of a particular market risk and credit. In this work, we study a model of risk measure in finance: Value at Risk (VaR), which is a new tool for measuring an entity's exposure risk. We explain the concept of value at risk, your average, tail, and describe the three methods for computing: Parametric method, Historical method, and numerical method of Monte Carlo. Finally, we briefly describe advantages and disadvantages of the three methods for computing value at risk.

Résumé: Managing and controlling risk is a topic research in the world of nance. Before a risky situation, the stakeholders needs to do comparison according to the positions and actions, nancial institutions must take measures of a particular market risk and credit. In this work, we study a model of risk measure in nance : Value at Risk (VaR), which is a new tool for measuring an entity's exposure risk. We explain the value at risk for continuous distribution.