Abstract:
The new probability function,which is named as L distribution,has been pointed out in this paper by comparing with another famous distribution such as normal(Gaussian) distribution,exponential distribution,uniform distribution,student distribution and so on.The main numerical characteristics of L distribution have been deduced in the paper.For example,mean value and variance etc have already been inferred here.Most physical system of being deviating from its equilibrium state,when in damping process generally should be identified as falling into L distribution.The total average of variable of the distribution is equivalent to zero,at this time this is defined as absolute equilibrium state.But since the function has infinite result at the point θ=0,which is supposed that the absolute equilibrium state essentially does not occur in this kind of system or in this kind of physical processes.In addition,continuous random variables concentrically(thickly) scatter in area near to zero θ=0,this is just an obvious character(quality) of L distribution and peculiar of L function differentiating from other renowned distribution.In a word,the new distribution function f(θ)=ln(θM/θ)2/(4θM) has been discovered in detail by author of this article,its mean square deviation is (θM/3)2,its mathematical expectation is zero and the coefficient of kurtosis of the distribution function is 0.24.the fourth moment v4=(θM)4/25,finally third moment and coefficient of skew are both zero.Also M-th moment exist.this article has several extension which follows below:The probability is equal 2/e=74.04% within coverage of 0 θ≤|θM/e|.The probability will be certainly nonexistent in the context of absolute Equilibrium θ=0.The probability will be biggest within the realm (area) in the vicinity of Quasi-Equilibrium State (θ→0=mathematical expectation).It was new trial that Quasi-Equilibrium state is put into probability for discussion in spite of general analyzed traditionally in dynamical balance way.Along with its application into atmospheric field,the non-dimensional number W is surfaced.