In this article, we introduce a new circular distribution to be called as wrapped Lindley distribution and derive expressions for characteristic function, trigonometric moments, coefficients of skewness, and kurtosis. Method of maximum likelihood estimation is used for the estimation of parameters. We carry out a simulation study to show that the obtained maximum likelihood estimator is consistent. The proposed model is also applied to a real-life dataset, and its performance is compared with that of wrapped exponential distribution.

In this article, we derive a new generalized geometric distribution through a weight function, which can also be viewed as a discrete analog of weighted exponential distribution introduced by Gupta and Kundu ( 2009 Gupta, R. D. , and D. Kundu. 2009. A new class of weighted exponential distributions. Statistics 43:621–34. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ). We derive some distributional properties like moments, generating functions, hazard function, and infinite divisibility followed by different estimation methods to estimate the parameters. New characterizations of the geometric distribution are presented using the proposed generalized geometric distribution. The superiority of the proposed distribution to other competing models is demonstrated with the help of two real count datasets.

In this article, we consider a single change point model for a sudden change in the hazard rate of Lindley distribution to model right-censored survival data. We derive the quantile function to generate random numbers from the proposed distribution by using the Lambert function. The maximum likelihood estimation method is used to estimate parameters of the change point model. A simulation study is also carried out to analyze the performance of the estimators. To validate our findings, a dataset on bone marrow transplant for patients of acute lymphoblastic leukemia is analyzed using the proposed model and is compared with the existing exponential single change point model.

The change–point problem is about identifying when a pattern or trend shifts in time–ordered data. In survival analysis, change–point detection focuses on identifying alterations in the distribution of time–to–event data, which may be subject to censoring or truncation. In this paper, we introduce a change–point in the hazard rate of the log–logistic distribution. The log–logistic distribution is a flexible probability distribution used in survival analysis, reliability engineering, and economics. It is particularly useful for modeling time–to–event data exhibiting decreasing hazard rates. We estimate the parameters of the proposed change–point model using profile maximum likelihood estimation. We also carry out a simulation study and Bayesian analysis using the Metropolis–Hastings algorithm to study the properties of the proposed estimators. The proposed log–logistic change–point model is applied to survival data from kidney catheter patients and acute myeloid leukemia (AML) cases. A late change–point with a decreasing scale parameter in the catheter data reflects an abrupt increase in risk due to delayed complications, whereas an early change–point with an increasing scale parameter in AML indicates high early mortality followed by slower hazard progression in survivors. We find that the log–logistic change–point model performs better in comparison to the existing change–point models.