This function is estimated using window functions in Parzen's method. It is equal to one over two pi times the Fourier transform of the characteristic function. Performing a double-sided Laplace transform-like operation on this function, but without the negative sign in the exponential, yields the moment-generating function
This function is estimated using window functions in Parzen's method. It is equal to one over two pi times the Fourier transform of the characteristic function. Performing a double-sided Laplace transform-like operation on this function, but without the negative sign in the exponential, yields the moment-generating function. For a random variable x, integrating x times this function of x over the sample space gives the expectation of x. The integral of this non-negative function over all possible inputs must equal one. This function can be found by differentiating the cumulative distribution function. For 10 points, name this function for a continuous distribution whose integral from a to b gives the probability that x lies between a and b, and thus can be thought of as giving the relative probability that a random variable has value x.
This function is estimated using window functions in Parzen's method.
probability density function [or pdf; prompt on probability function]