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

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?

 

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