Cells with more gene mutations may stop functioning normally and grow to an uncontrollable size, resulting in cancer. Often individuals enquire about their survival chances after being diagnosed with cancer. While there are numerous aspects that go into determining an answer, statistics can come into aid. Statistics are numerical representations of what occurs in large  groups of people who have the same diagnosis and can provide an insight into what to expect. Survival statistics are used by doctors to determine a patients prognosis. The prognosis refers to the likelihood of recovery. Keeping this in mind, we have studied the applications of  a one parametric trigonometric model named as the sine modified Lindley (S-ML) distribution in this paper. This model is of great importance as it is based on the functionalities of the sinusoidal transformation and modified Lindley distribution. Secondly, it has a single parameter, which reduces the complexity of the model. We  have found that the new model is useful in modelling the survival times of patients undergoing cancer and chemotherapy sessions by using the method of goodness of fit. In addition, the model is seen to have a good fit in modelling growth hormone data in children. We believe that this model will be helpful for modelling the survival times of diseases similar to cancer and also in various aspects of biological data.

Keywords: Lindley distribution, Trigonometric function, Cancer data, Gene mutations, Growth hormone data, Goodness of fit.

Abbreviations: DNA, S-ML, MLE.