ABSTRACT
In this chapter, we discuss some commonly used probability distributions. We will see that, while discussing a particular probability distribution, we essentially deal with a family of probability distributions indexed by one or more parameters. This family of distributions gives us some liberty to vary the parameter value(s) while staying with a particular functional form. As a result, when it comes to model the outcomes of an experiment (i.e., approximating the actual probability distribution of a random variable), we can choose a suitable parameter value that can give the resultant, commonly used probability distribution a good fit to the actual one. Hence, to emphasize the role of the parameter(s) and keep track of the parameter(s), a typical pdf or pmf will be denoted by, for example, f(x| θ) instead of f(x), where θ is a relevant parameter involved in the probability distribution. If there is a single parameter involved, then θ is taken as scalar valued, otherwise θ is taken as vector valued. The collection of all possible values of θ, denoted by Θ, which makes f(x| θ) a pdf or pmf, is called the (natural) parameter space of the probability distribution f(x| θ). For the sake of simplicity, we take θ as scalar valued only, but if a situation demands, then θ can be vector valued too.
