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 Probability models
This module will be used where data distribution may not be normal, when normality is in doubt, or when type of distribution is known apriori, but the parameters of the distribution are needed. This module is essential when risk of exceeding a given value is to be assessed.

Probability models - Pdf manual

Example:
Hg concentration in soil samples

Task: Find the true value and a 99% quantile of the distribution. What is the risk of exceeding the limit concentration of 8mg/kg?
Data:
 ID Hg_Concentration TE_R-006 1.1.1966 TE_R-617 1.1.1956 TE_R-512 1.1.1966 TE_R-807 1.1.1952 TE_R-271 1.1.1956 TE_R-624 1.1.1956 TE_R-908 1.1.1933 TE_R-911 1.1.1947 TE_R-945 1.1.1961 TE_R-753 1.1.1966 TE_R-449 1.1.1966 TE_R-692 1.1.1970 TE_R-272 1.1.1966 TE_R-781 1.1.1980 TE_R-823 1.1.1966 TE_R-117 1.1.1961 TE_R-968 1.1.1989 TE_R-389 2.8.2009
Dialog window:

Protocol:
 Probabilistic models Maximum likelihood method (MLE) Task name : Sheet1 Data: All List of analyzed distributions Symetric models Parameters Distribution Likelihood P-P correlation A B Normal -181,6785248 0,9093237246 23673,33333 6015,475161 Cauchy -180,2259792 0,9442434739 23673,33205 2058,729961 Logisitic -180,7001734 0,9283511579 23673,33324 2987,734462 Laplace -179,1624181 0,9243167929 24107,99995 3867,519046 Uniform -184,3012672 0,7858115537 12055 40027 Asymetric models Parameters Distribution Likelihood P-P correlation A B C Gamma -183,4977216 0,8804793092 9257,800497 5645,342342 2,802049929 Gumbel -181,3723066 0,9240551682 20873,80725 5090,558443 Triangular -181,7168227 0,880124682 9807,619917 41968,85541 23511,5318 Exoponential -186,4862994 0,7621335177 12054,87945 11618,45345 Weibull -182,1741659 0,8941368252 3123,866839 22986,89688 3,594183413 Lognormal -180,950687 0,926506368 -10233,34365 10,41711622 0,1680905563 Sample moments Mean Variance Skewness Kurtosis Median 23673,33333 36185941,41 0,9698171422 5,284355292 24108 Model moments Distribution Mean value Variance Skewness Kurtosis Median Modus Normal 23673,33333 36185941,41 0 3 23673,33333 23673,33333 Cauchy not def. not def. not def. not def. 23673,33205 23673,33205 Logisitic 23673,33324 29367196,12 0 4,2 23673,33324 23673,33324 Laplace 24107,99995 29915407,14 0 6 24107,99995 24107,99995 Uniform 26041 65202732 0 1,8 26041 not def. Gamma 25076,33161 89301023,48 1,194791325 2,141289467 - 19430,98927 Gumbel 23812,1573 42626468,18 1,1395 5,4 22739,56269 20873,80725 Triangular 25096,00238 43411529,56 0,1428981506 2,4 24740,82112 23511,5318 Exoponential 23673,3329 134988460,6 2 9 20108,1777 12054,87945 Weibull 23835,67984 40954627,69 0,001959281692 2,716462326 24968,10965 25091,4316 Lognormal 23669,13593 32938162,92 - - 23193,55545 22262,31508 Quantiles and probability Distribution Probab(x=8) Quant(0,01) Quant(0,99) Normal 4,175876848E-005 9679,247478 37667,41919 Logisitic 0,0003629694598 9944,338116 37402,33085 Cauchy 0,02762135151 -41836,51353 89183,17716 Laplace 0,0009833631026 8978,180302 39237,82262 Uniform 0 12334,72 39747,28 Gamma 0 11346,09658 54687,48048 Gumbel 6,648953412E-027 13099,61245 44291,1337 Triangular 0 11906,98456 39532,43967 Exoponential 0 12171,64959 65559,83166 Weibull 0 9515,806658 38280,99613 Lognormal 9,789946631E-013 12375,1088 39188,77047
Graphical output: