DISTRIBUTION FUNCTION

The distribution of a set of numerical values shows how they are distributed over real numbers and it is completely characterized by the empirical distribution function. The probability distribution of a random variable is defined by its probability distribution function (PDF). For each real value of x, the cumulative distribution function of a set of numerical data is the fraction of observations that are less than or equal to x, and a plot of the empirical distribution function is an uneven set of stairs, with the width of the stairs as the spacing between adjacent data. The height of the stairs depends on how many data points have exactly the same value. The distribu­tion function is zero for small enough (negative) values of x, unity for large enough values of x, and increases monotonically. If y > x, the empirical distribution function evaluated at y is at least as large as the empirical distribution function evaluated at x.