GB1335072A - Method and apparatus for determining the probability density function and the distribution function of a random variable - Google Patents

Abstract

1335072 Determining distribution functions and probability density functions SOC FRANC AISE D'EQUIPEMENTS POUR LA NAVIGATION AERIENNE 26 May 1971 [27 May 1970] 17318/71 Heading G1U An estimate of the distribution function F(x) and the probability density function P(x) of a random variable X is obtained by - (1) converting a sequence of values of the variable into an electric signal X(t) having a corresponding time varying amplitude C, Fig. 1, (2) for each of the sequence of n equal intervals #T j (a) determining the total duration of time for which X(t) lies between two threshold levels X j and X j + #X, this being achieved by comparing the signal X(t) with the levels X j and X j + #X in two comparators 4, 3 respectively, Fig. 2, and thereby producing, by an exclusive OR gate 6, pulses (see Fig. 1 bottom graph) whose integral 8, Fig. 2, has a value proportional to the duration required, and (b) determining the total duration of time for which the signal X(t) is below the threshold level X j , this being achieved by integrating 7, Fig. 2, the pulses (see graph b, Fig. 1) produced by the comparator 4, the threshold levels X j being such that X j + 1 = X j + #X and (3) plotting the resulting durations as a sequence of ordinates, for example on a graphical recorder driven at constant speed, to provide the required estimates, typical results being shown in Fig.4b.