Tabaistic regression and its application to the space shuttle Challenger O-ring data

Abstract

In this paper, we introduce a new family of probability distributions called the tabaistic family of distributions. The members of this family can have either unimodal or bimodal probability density functions. This family can be used when the data comes from a skewed or bimodal distribution. A major application of the unimodal member of this family is in the analysis of binary or polytomous response data when covariates are present. The logistic regression (Hosmer, D.W., Lemeshow, S.: Applied Logistic Regression. Wiley, New York (2000)) and probit analysis (Finney, D.J.: Probit Analysis. Cambridge University Press, Cambridge (1971)) are widely used when the distribution is symmetric. When the distribution is asymmetric, the tabaistic regression will be a better choice. We apply the tabaistic regression to analyze the space shuttle Challenger O-ring data and will compare the results with the logistic regression and the probit analysis models.