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Abstract:
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We consider probability density function of some statistical models where the parameters are uncertain. The estimates of these uncertain parameters can be point estimates or interval estimates. Buckley (2004) introduced a method of estimation of parameters in parametric models, using a set of confidence intervals producing a triangular shaped fuzzy number for the estimator. In this paper, following Buckley (2004), we model the uncertainty in model parameters by using fuzzy number estimates for the parameters, and obtain the fuzzy probability density functions. This will be discussed for log-normal and inverse Gaussian distributions. The computation of several fuzzy statistical measures such as fuzzy mean, variance, skewness, kurtosis, etc. of these distributions will be illustrated through numerical examples.
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