High Quality Content by WIKIPEDIA articles! n probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution. In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable when the variable is discrete, or the probability of the value falling within a particular interval when the variable is continuous. The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any subset of that range.