Parametric Statistical Model Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

Parametric statistical model, or a set of assumptions, is a family of distribution functions indexed by a set of unknown parameters. In other words, parametric statistical model is the distribution derived from the set of probability distributions that corresponds to the set of variables reflecting the variables’ relationship in the model.

It is assumed that the set of parameters uniquely identifies the resulted distribution, parametric statistical model, and the estimates of parameters are based on data from the resulted distribution, parametric statistical model. For example, the normal parametric statistical model is the normal distribution, one of the important probability distributions in statistics. Other examples include the exponential model (the exponential distribution), the log-normal model (the log-normal distribution), the Weibull model (the Weibull distribution), and the gamma model (the gamma distribution).

The main advantage of parametric modeling is the availability of the estimators based on the assumed probability distribution, which makes statistical inferences easier. However, a parametric model might not accurately represent the true distribution of data, which could lead to the biased estimates of parameters and erroneous statistical inferences. By contrast, nonparametric statistical model is distribution free, and therefore could capture better the true distribution of data, though not without some drawbacks: it is less efficient or powerful than parametric models and unable to extrapolate beyond the available data sample, which prevents making strong quantitative statements.

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