In this article, we introduce a weighted version of the Xgamma exponential distribution, extending its utility in modeling lifetime data. We derive several important distributional properties of the proposed model, including moments, residual life functions, generating functions, stochastic ordering, aging intensity, and entropy. These properties provide deeper insights into the behavior and structure of the proposed distribution. To estimate the model parameters, we discuss the maximum likelihood estimation approach, focusing on complete sample data. To demonstrate the practical applicability of the proposed distribution, we analyze two real-world lifetime data sets. The performance of the weighted Xgamma exponential distribution is compared with several well-established one- and two-parameter lifetime distributions, along with their weighted versions. Additionally, comparisons are made with length-biased and area-biased lifetime distributions to further assess the robustness of the proposed model. The results of these comparisons indicate that the proposed weighted distribution offers a superior fit, particularly for data sets exhibiting an increasing failure rate. The model’s ability to outperform competing distributions highlights its potential as an effective alternative for analyzing lifetime data in reliability and survival studies.
The inaccuracy measure has recently become a valuable tool for detecting errors in experimental data. This measure applies only when random variables have density functions. To circumvent this constraint, the cumulative inaccuracy measure is a commonly used alternative measure of inaccuracy in the literature. When the observations generated by a stochastic process are recorded using a weight function, weighted distributions are established. Based on right-censored dependent data, we provide a nonparametric estimate for the weighted dynamic cumulative past inaccuracy measure in this study. The proposed estimator’s asymptotic characteristics have been examined, and its performance demonstrated through simulated and real-world data sets.
The game of cricket is enjoyed by millions of fans across the Globe. India is perusing the game like anything. Though, at present, many local tournaments like IPL were conducted in India, the ability of the batsmen and their patterns of scoring runswere reflected by the amount of runs they score in the international ODI’s played between Countries. The runs scored by batsmen with information on whether they are “batting-first” or “chasing” throws more light on the patterns of runs-scoring. Also, the order in which the batsmen bat is also taken into consideration in this study. Further, the performance of batsmen varies across different teams of the game. More uncertainty exists in the run-scoring pattern. All these make it difficult for predicting the runs scored by a batsman. Survival analysis comes handy in predicting the probabilities of such events. The study, in this perspective, considers nine batsmen selected from the one-day Indian world cup squad 2023. The information of these batsmen, particularly the runs scored by them against different countries were used to find the probabilities of their run-scoring pattern. The study uses Kaplan-Meier’s product limit estimator, Cox Proportional Hazard model and Accelerated Failure Time Parametric model for analysing the patterns. Log-rank test is used for comparing survival distributions. Also, the study compares the relative performance of selected batsmen. Data, updated as on 4th September 2023, were used for each of the batsman under consideration. The analysis has been carried out using R program.
