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Lindley distribution has been a popular distribution, and many of its generalizations are well established in the literature. The wrapped Lindley distribution has also been a good alternative to the existing circular models. Looking at the utility and applicability of the Lindley distribution, in this paper, we introduce a new circular distribution, namely the alternate-wrapped Lindley (AWL) distribution. This distribution is generated by using the alternate wrapping method (Joshi and Rattihalli (2022)) on the Lindley distribution. The properties of the AWL model are derived, and the maximum likelihood estimator of the model parameter is obtained. To check the performance of the estimator, a simulation study is performed. The proposed model is then compared with other circular models with the help of real data analysis. Keywords: Akaike Information Criterion (AIC); Alternate Wrapped Exponential (AWE) Distribution; Lindley Distribution; Rose Diagram; Wrapped Lindley (WL) Distribution

MSC Classification: 60E05 , 62E10.

This study introduces the Modified Exponential-Gamma (ME-G) distribution, a novel one-parameter lifetime model constructed as a mixture of an exponential and a gamma distribution with fixed shape parameter 7. Motivated by the limitations of existing one-parameter models in capturing complex lifetime behaviours, the ME-G distribution aims to provide enhanced flexibility and improved fit for reliability and survival data. Key statistical properties, including probability density, survival, hazard, and moment functions, are derived and examined. Parameter estimation is performed using both Maximum Likelihood Estimation (MLE) and the Metropolis-Hastings (M-H) algorithm, with the M-H algorithm demonstrating superior goodness-of-fit performance. Comparative analyses against established one-parameter distributions such as Suja, Rama, Akash, Lindley, and Exponential, using real aircraft window glass strength data and simulated datasets confirm the ME-G distribution’s superior fit as indicated by lower information criterion scores. The results highlight the ME-G distribution’s potential as a robust alternative for lifetime modelling, especially when conventional models fall short. This work advances lifetime distribution theory by combining analytical tractability with practical efficacy, offering a promising tool for future reliability and survival analysis.

Keywords: Lifetime distribution, Moments, Hazard rate function, Survival function, Stress-strength reliability, Metropolis-Hasting algorithm.
Subject Classification: 62E15, 65C05.
 

For the purpose of estimating the finite population mean, a new ratio estimator has been proposed wherein a known coefficient of variation of study variable is used. The proposed ratio estimator is shown to be less biased than the conventional ratio estimator under suitable conditions. The estimator is found to be more efficient than the exponential ratio estimator under condition that holds good in practice very often. Empirical investigations supporting the proposed estimator from the standpoint of percent relative bias or mean squared error have been carried out in respect of several populations, natural and artificial.

Keywords: Finite population, ratio estimator, coefficient of variation, percent relative bias, means squared error
Subject classification code: 2613