The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance.

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided.

This paper is devoted to the properties and applications of a new one-parameter discrete distribution with support on integers. The new distribution represents a discrete analogue of the double Lindley distribution, a symmetric version of the negative binomial distribution and a weighted version of the Inusah-Kozubowski distribution. Some properties of the new distribution are derived, such as log-concavity, mode(s), cumulative density function, quantile function, probability generating function, raw moments, skewness, kurtosis, and order statistics. The parameter of the distribution is estimated by the maximum likelihood method. The usefulness of the new distribution is illustrated by means of two practical datasets with integer values on ℤ, namely stock exchange and flood data.