statistical calculations to prove normal distribution

Some examples of random variables for which the Poisson distribution is assumed to apply are: the number of particles emitted from a radioactive source in a given time, the number of typing errors per page of manuscript, the number of calls received at a telephone exchange in a given time period, the number of goals scored by a particular team in a football match. This discrete distribution relates to the number of events that occur in a given interval of time or space when the events occur randomly (in time or space) at a certain average rate. Johnson and Kotz may find some details about these distributions in the textbook. These distributions cover all types of data commonly used in practice. In this section the point and interval estimates for one discrete and five continuous distributions are described. Then the normality assumption is not warranted. We shall describe some of the most useful probability density functions that the user may meet in the practice, Usual assumption is that data are from normal distribution, but there are some tasks when the random quantity is constrained on one side, or it must be in finite interval. Under favorable circumstances in the EDA, the experimental data are associated with a known function, a probability density function, which corresponds reasonably with the data. Users would like to replace a large volume of experimental data with a few easily grasped numbers. Milan Meloun, Jiří Militký, in Statistical Data Analysis, 2011 3.3 Point and Interval Estimators for Selected Distributions

Statistical calculations to prove normal distribution