Edward .G. NjengaJaffer, Meymuna Shariff2023-08-072023-08-072023http://ir-library.ku.ac.ke/handle/123456789/26572A Research Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science (Statistics) in the School of Pure and Applied Science of Kenyatta University, June 2023The project considers the MLEs for Kumaraswamy distribution centered on PTHCS using the expectation maximization algorithm. A two parameter Kumaraswamy distribution can be applied in natural phenomena that have outcomes with an upper and a lower bound. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. The field of survival analysis has advanced over the years and extensive research has been undertaken. Previously, maximum likelihood estimator of various distributions has been done using methods like Newton-Raphson, Bayesian inference and EM algorithm. The application of these techniques in survival analysis is mainly intended to save on costs and duration taken in an experiment. Based on PTHCS, MLEs of Kumaraswamy distribution are obtained via EM algorithm. EM algorithm has been utilized in manipulation of missing data as it is a more superior method when handling incomplete data. Comparison of different combinations of censoring schemes with respect to the MSEs and biases at fixed parameters of  and  are obtained through simulation. It is observed that in the three censoring schemes, for an increasing sample size, the MSEs and biases are generally decreasing. Eventually, an illustration with real life data set is provided and it illustrates how MLEs works in practice under different censoring schemes. It is apparent from the observations made that the estimated values of ^ and ^ increases from scheme one to scheme three.enMaximum Likelihood EstimationParameters for Kumaraswamy DistributionProgressive Type Ii Hybrid Censoring SchemeThesis