Normal Distribution

Abstract

The normal distribution is probably the most popular statistical distribution. It is also known as the Gaussian distribution or error function. Many statistical parameters are found to be approximately normally distributed; therefore, the normal distribution is often used for statistical inferences. A variety of natural phenomena either approximately follow a normal distribution or can be transformed to follow a normal distribution. One of the earliest applications of the normal distribution in hydrology was made by Hazen (1914), who introduced the normal probability paper for ananlysis of hydrologic data. Markovic (1965) fitted the normal distribution to annual rainfall and runoff data Slack et al. (1975) showed that when the information about the distribution of floods and economic losses associated with the design of flood retardation structures was lacking, it was better to use the normal distribution than other distributions such as extreme value, lognormal, Weibull, etc. The other advantages of the normal distribution are that it is extensively tabulated and the standardized normal variate is the same as the frequency factor.