Transformed Normal Probability Density Functions for Parameter Estimation

The transformation of a normal density function into probability density function for parameter estimation, is presented. Parameter-estimation, for determination of the aircraft performance and control, depends on the probability density function, which can provide accurate information about model uncertainties and measurement errors. The probability density function is derived from a normal density function by adjusting the order of the exponentiation, separating the function in left- and right-hand tolerance sides, and correcting the scale factor. It was observed that the transformed probability density function can provide two additional degrees of freedom with respect to the Gaussian probability density function. The transformed probability density function can be used for modeling the boundary conditions for parameter estimation.