A Novel Approach to the Quasi-Garima Distribution: Properties and Applications

The study of failure times is essential in evaluating the reliability and longevity of components in engineering systems. Reliability analysis relies on probability models to predict the likelihood of failure within a given time frame. Length biased probability distributions arise in scenarios where the probability of sampling an object or event is directly proportional to its length, size or duration. These distributions are especially relevant in areas such as reliability theory, survival analysis, and epidemiology. The mathematical framework of length-biased distributions is based on transforming the probability density function of a baseline distribution by weighting it according to the length of the object. In this paper, we obtained a novel length biased probability distribution, the length biased quasi Garima distribution, characterized by two parameters. We explored and derived its statistical properties including moments, moment generating function, characteristic function, hazard rate function and survival function. Further we also studied about order statistics and entropy measures. We estimated distribution parameters using maximum likelihood estimation method. We presented the likelihood ratio test for comparing the goodness of fit of the length biased quasi Garima distribution over quasi Garima distribution. Additionally, we performed simulation study to evaluate the reliability of maximum likelihood estimators. Finally, length biased quasi Garima distribution is applied to a real-life data set related to failure time. the distribution proved to be a better fit than other established well-known distributions.