Dissertation (MSc Statistics)The purpose of this study was to find out the appropriate probability distributions that fit suitable to the motor insurance claims in respect of motorcycles, cars, and heavy vehicle insurance claimed amounts. The specific objectives were: to estimate the probability distributions considered, to identify appropriate model that fit best to the motor insurance claims amounts among eight distributions and to test the goodness of fit of the fitted probability distribution models. Daily data were collected from Britam Insurance Company Limited (T) from January 2007 to December 2016 of Dar es Salaam region. The estimates of parameters of the distributions were obtained by using maximum likelihood estimation method, and Kolmogorov-Sminov test statistic was used to fully assess the goodness of fit of eight probability distributions considered at 5% level of significance. Appropriate probability distribution model has been identified based on model selection criteria developed. Empirical Distribution Function (EDF) and Cumulative Distribution Function (CDF) plots were also used to visually assess the goodness of fit of the distribution models. The log likelihood values and Akaike’s information criterion were obtained and used as the selection criteria of the model that fit best the motor insurance claimed amounts. The model with large log likelihood value was considered to be the better model or the model with minimum AIC was considered to be the better model for motor insurance claimed amounts. These data were analysed by using SAS version 9.4, and SPSS version 21. The results showed that the Lognormal distribution fitted best to the motorcycle insurance claimed amounts and Inverse Gaussian distribution model fitted best to the car and heavy vehicle insurance claim amounts respectively.