Burr distribution is Burr Type XII distribution which is one among the twelve types of the continuous distributions in Burr system. It has two positive shape parameters, namely k and c. It is implied from the probability density function which can be either decreasing or unimodal, and the hazard rate function which can be either decreasing or upside-down bathtub-shaped. The other distributional properties and the moment properties of Burr distribution will be discussed in more detail. By considering these properties, we will study its tail behaviour. To estimate the parameters k and c, the maximum likelihood method will be considered. Based on the properties of the data representing the remission time of bladder cancer patients, we infer that Burr distribution is suitable to model the data. The goodness-of-fit using the Kolmogorov–Smirnov test shows that Burr distribution fits well to the data.

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Poisson Regression analysis is commonly used for dependent variable that has non-negative value, called count data. Poisson Regression has an assumption that mean of dependent variable equal to its variance. On over dispersion case where the variance is greater than mean, poisson regression is inconvenient to used because it may underestimate the standard error of regression parameters and consequently giving misleading inference. Poisson-Inverse Gaussian and Negative Binomial regression model can be used on over dispersion data. This paper will discuss about Poisson-Inverse Gaussian regression model, Negative Binomial regression model and comparing them in terms of Goodness-of-fit (GOF) statistics on case study of horseshoe crabs data. According to the result, pseudo R-squared value of P-IG regression model is greater than the Negative Binomial regression model. It shows that P-IG regression model is better than Negative Binomial regression model.