Journal of Data Science

Abstract: Simulation studies are important statistical tools used to inves-tigate the performance, properties and adequacy of statistical models. The simulation of right censored time-to-event data involves the generation of two independent survival distributions, where the rst distribution repre-sents the uncensored survival times and the second distribution represents the censoring mechanism. In this brief report we discuss how we can make it so that the percentage of censored data is previously de ned. The described method was used to generate data from a Weibull distribution, but it can be adapted to any other lifetime distribution. We further presented an R code function for generating random samples, considering the proposed approach.

Abstract: In any sport competition, there is a strong interest in knowing which team shall be the champion at the end of the championship. Besides this, the end result of a match, the chance of a team to be qualified for a specific tournament, the chance of being relegated, the best attack, the best defense, among others, are also subject of interest. In this paper we present a simple method with good predictive quality, easy implementation, low computational effort, which allows the calculation of all the interesting quantities above. Following Lee (1997), we estimate the average goals scored by each team by assuming that the number of goals scored by a team in a match follows a univariate Poisson distribution but we consider linear models that express the sum and the difference of goals scored in terms of five covariates: the goal average in a match, the home-team advantage, the team’s offensive power, the opponent team’s defensive power and a crisis indicator. The methodology is applied to the 2008-2009 English Premier League.

Overdispersion is a common phenomenon in Poisson modelling. The generalized Poisson (GP) distribution accommodates both overdispersion and under dispersion in count data. In this paper, we briefly overview different overdispersed and zero-inflated regression models. To study the impact of fitting inaccurate model to data simulated from some other model, we simulate data from ZIGP distribution and fit Poisson, Generalized Poisson (GP), Zero-inflated Poisson (ZIP), Zero-inflated Generalized Poisson (ZIGP) and Zero-inflated Negative Binomial (ZINB) model. We compare the performance of the estimates of Poisson, GP, ZIP, ZIGP and ZINB through mean square error, bias and standard error when the samples are generated from ZIGP distribution. We propose estimators of parameters of ZIGP distribution based on the first two sample moments and proportion of zeros referred to as MOZE estimator and compare its performance with maximum likelihood estimate (MLE) through a simulation study. It is observed that MOZE are almost equal or even more efficient than that of MLE of the parameters of ZIGP distribution.

A new flexible extension of the inverse Rayleigh model is proposed and studied. Some of its fundamental statistical properties are derived. We assessed the performance of the maximum likelihood method via a simulation study. The importance of the new model is shown via three applications to real data sets. The new model is much better than other important competitive models.