Interplanetary electron beams, produced by CMEs and flares, are unstable in the solar wind and generate Langmuir waves at the local plasma frequency (f_p) or its harmonic (2f_p). Radio observations of the waves in the range 4 - 256 kHz from the WAVES experiment onboard the WIND spacecraft have been statistically analyzed. A subset of 36 events has been selected for this study. The background consisting of thermal noise, type III bursts and Galactic background has been removed and the remaining power spectral density has been fitted by Pearsons system of probability distributions. The coefficients of the probability distributions have been calculated by using two methods: method of moments and maximum likelihood estimation method. We have shown that the probability distributions of the power spectral density of the Langmuir waves belong to three different types of Pearsons probability distributions: type I, type IV and type VI. In order to compare the goodness of the fits, a few statistical tests have been applied, showing for all of the considered events that the Pearsons probability distributions fit the data better than the Gaussian ones. This is in contradiction with the Stochastic Growth Theory which predicts log-normal distribution for the power spectral density of the Langmuir waves. The uncertainty analysis that has been performed also goes in favor of the use of Pearsons system of distributions to fit the data.