*Article* **The Sine Modified Lindley Distribution**

**Lishamol Tomy 1, Veena G <sup>2</sup> and Christophe Chesneau 3,\***


**Abstract:** 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.

**Keywords:** goodness-of-fit; trigonometric distributions; modified Lindley distribution; engineering data; climate data; statistical analysis
