• ### Standard L Probability Distribution Function

Wan-Li Wang (w.-l. Wang),Ying-Qi Xie (Y.-Q. Xie), Xiao-Min Ye (X.-M. Ye), Ling Luo (L. Luo)

Abstract: The cumulative distribution function(cdf) table is very important and also fundamental tool for any distribution theory, in fact, it is enable one to calculate the probability between a and b after cumulative distribution function is deduced, therefore, it is very easily and conveniently to obtain the probability between a and b using distribution function table, such as P(a≤ z ≤b) = F(b) − F(a). L Distribution Function is newest and original distribution theory whose unique properties are illustrated as: its continuous random variable is limited, non-standard variable fall into interval of positive most amplitude and negative most amplitude(also including most amplitude ), but standard variable interval is between positive one (+1) and negative one ( -1) (also including ±1), standardized deviation is 1/3;the probability reaches 70% in the interval of (-1/3,+1/3); the probability is only 3% in the interval exceeding double standardized deviation 2/3;its distribution is more concentrated than Normal Distribution does around mean value; its coefficient of kurtosis is 0.24, in addition, there are different the scale parameter in two sides of mean value after the variable is standardized, two kinds of different the scale parameter is determined by the features of limited variable and by the boundary conditions of distribution equations when continuous random variable is equal to maximum and minimum respectively.

Keywords: Cumulative distribution function (cdf) table, compute probability, application of probability, amount of probability, equipment of statistical calculating.