【作者】 王万里； 谢应齐；

【Author】 Wan Li Wang;YingQi Xie;School of Resource and Environmental Science of Wuhan University;China Meteorological Administration,Wuhan Regional Climate Centre;College of Earth Science,Yunnan University;

【机构】 武汉区域气候中心； 武汉大学资源与环境科学学院； 云南大学地球科学学院；

【摘要】 分布函数表是分布理论中的重要组成部分和基础性工具,知道分布函数事实上就能计算任意区间随机事件的发生概率,分布函数表省略了这一计算过程,把计算简变成查阅,由任意两点所查得的分布值相减进而求出两点(a,b)间的概率,即P(a≤z≤b)=F(b)-F(a)。L分布作为一刚问世的新分布函数,基本特点是自变量取值区间有界,非标准化的自变量取值范围介于正负最大振幅之间(含最大振幅),标准(0,1)化的自变量取值范围介于正负1之间(含正负1);而它的均方差是1/3,或1/3最大振幅,在正负均方差之间其发生概率高达70%,而在两倍均方差外发生概率分别只有6%,在均值附近L分布比正态分布更为集中,其峰度系数比正态分布高0.24,另外L分布自变量标准(0,1)化后,表现出在均值两侧要取不同尺度参数的特殊性质,这点是由自变量有界和取最大最小值时的边界条件所控制。更多还原

【Abstract】 The cumulative distribution function(cdf) table is very important and also fundamental tool for any distribution theory, in fact, it is enable anybody 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 is1/3;the probability reaches 70% in 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.更多还原