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Merge pull request #316 from jecisc/divers-cleanings

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/src/Math-Distributions/PMStudentDistribution.class.st

Class {
        #name : #PMStudentDistribution,
        #superclass : #PMProbabilityDensity,
        #instVars : [
                'degreeOfFreedom',
                'norm',
                'chiSquareDistribution',
                'incompleteBetaFunction'
        ],
        #category : #'Math-Distributions-ForHistogram'
}

{ #category : #creation }
PMStudentDistribution class >> asymptoticLimit [

        ^30
]

{ #category : #creation }
PMStudentDistribution class >> degreeOfFreedom: anInteger [
        "Create a new instance of the receiver with anInteger degrees of freedom."

        ^anInteger > self asymptoticLimit
                ifTrue: [PMNormalDistribution new]
                ifFalse:
                        [anInteger = 1
                                ifTrue: [PMCauchyDistribution shape: 0 scale: 1]
                                ifFalse: [super new initialize: anInteger]]
]

{ #category : #information }
PMStudentDistribution class >> distributionName [

        ^'Student distribution'
]

{ #category : #creation }
PMStudentDistribution class >> fromHistogram: aHistogram [
        "Create an instance of the receiver with parameters estimated from the given histogram using best guesses. This method can be used to find the initial values for a fit."
        | dof var |
        var := aHistogram variance.
        var = 0
                ifTrue: [ ^nil].
        dof :=  ( 2 / (1 - (1 / aHistogram variance))) rounded max: 1.
        ^dof > self asymptoticLimit ifTrue: [ nil]
                                                                ifFalse:[ self degreeOfFreedom: dof]
]

{ #category : #creation }
PMStudentDistribution class >> new [

        ^self error: 'Illegal creation message for this class'
]

{ #category : #creation }
PMStudentDistribution class >> test: aStatisticalMoment1 with: aStatisticalMoment2 [
        "Perform a consistency Student test (or t-test) on the averages of  two statistical moments ( or histograms). Answers the probability of failing the test."
        | t |
        t := ( aStatisticalMoment1 average - aStatisticalMoment2 average) abs.
        ^1 - ( ( self class degreeOfFreedom: (  aStatisticalMoment1 count + aStatisticalMoment2 count - 2)) acceptanceBetween: t negated and: t)
]

{ #category : #information }
PMStudentDistribution >> average [

        ^0
]

{ #category : #transformation }
PMStudentDistribution >> changeParametersBy: aVector [
        "Modify the parameters of the receiver by aVector."
        degreeOfFreedom := degreeOfFreedom + ( aVector at: 1).
        self computeNorm
]

{ #category : #information }
PMStudentDistribution >> chiSquareDistribution [
        "Answer the chi square distribution used to generate random numbers for the receiver."

        chiSquareDistribution ifNil: [ chiSquareDistribution := PMChiSquareDistribution degreeOfFreedom: degreeOfFreedom - 1 ].
        ^ chiSquareDistribution
]

{ #category : #private }
PMStudentDistribution >> computeNorm [
        "Private - Compute the norm of the receiver because its parameters have changed."
        norm := ( ( degreeOfFreedom / 2 logBeta: ( 1 / 2) ) + ( degreeOfFreedom ln / 2)) negated
]

{ #category : #information }
PMStudentDistribution >> confidenceLevel: aNumber [
        "Answer the probability in percent of finding a value distributed according to the receiver with an absolute value larger than aNumber."
        ^( 1 - ( self symmetricAcceptance: aNumber abs)) * 100
]

{ #category : #information }
PMStudentDistribution >> distributionValue: aNumber [
        "Answers the probability of observing a random variable distributed according to the receiver with a value lower than or equal to aNumber."
        aNumber = 0
                ifTrue: [ ^1/2].
        ^( aNumber > 0
                ifTrue: [ 2 - ( self symmetricAcceptance: aNumber abs)]
                ifFalse:[ self symmetricAcceptance: aNumber abs]) / 2
]

{ #category : #information }
PMStudentDistribution >> incompleteBetaFunction [
        "Private - Answers the incomplete beta function used to compute the symmetric acceptance integral of the receiver."

        incompleteBetaFunction ifNil: [ incompleteBetaFunction := PMIncompleteBetaFunction shape: degreeOfFreedom / 2 shape: 0.5 ].
        ^ incompleteBetaFunction
]

{ #category : #initialization }
PMStudentDistribution >> initialize: anInteger [

        anInteger > 0
                ifFalse: [ self error: 'Degree of freedom must be positive'].
        degreeOfFreedom := anInteger.
        self computeNorm.
        ^self
]

{ #category : #information }
PMStudentDistribution >> kurtosis [
        "Answer the kurtosis of the receiver. Undefined if the degree of freedom is less than 5."
        ^degreeOfFreedom > 4 ifTrue: [ 6 / ( degreeOfFreedom - 4)]
                                                 ifFalse:[ nil]
]

{ #category : #information }
PMStudentDistribution >> parameters [

        ^Array with: degreeOfFreedom
]

{ #category : #information }
PMStudentDistribution >> random [
        "Answer a random number distributed according to the receiver."
        ^PMNormalDistribution random * ( ( (degreeOfFreedom - 1) / self chiSquareDistribution random ) sqrt)
]

{ #category : #information }
PMStudentDistribution >> skewness [

        ^0
]

{ #category : #information }
PMStudentDistribution >> symmetricAcceptance: aNumber [
        "Compute the acceptance of the receiver between -aNumber and aNumber"
        ^ self incompleteBetaFunction value: ( degreeOfFreedom / ( aNumber squared + degreeOfFreedom))
]

{ #category : #information }
PMStudentDistribution >> value: aNumber [
        "Answers the probability that a random variable distributed according to the receiver gives a value between aNumber and aNumber + espilon (infinitesimal interval)."
        ^( norm - ( ( aNumber squared / degreeOfFreedom + 1) ln * ( ( degreeOfFreedom + 1) / 2))) exp
]

{ #category : #information }
PMStudentDistribution >> variance [
        "Answer the variance of the receiver. Undefined if the degree of freedom is less than 3."
        ^degreeOfFreedom > 2
                ifTrue: [ degreeOfFreedom / ( degreeOfFreedom - 2)]
                ifFalse:[ nil]
]

1	Class {
2	#name : #PMStudentDistribution,
3	#superclass : #PMProbabilityDensity,
4	#instVars : [
5	'degreeOfFreedom',
6	'norm',
7	'chiSquareDistribution',
8	'incompleteBetaFunction'
9	],
10	#category : #'Math-Distributions-ForHistogram'
11	}
12
13	{ #category : #creation }
14	PMStudentDistribution class >> asymptoticLimit [	3✔
15		3✔
16	^30	3✔
17	]	3✔
18
19	{ #category : #creation }
20	PMStudentDistribution class >> degreeOfFreedom: anInteger [	3✔
21	"Create a new instance of the receiver with anInteger degrees of freedom."	3✔
22		3✔
23	^anInteger > self asymptoticLimit	3✔
24	ifTrue: [PMNormalDistribution new]	3✔
25	ifFalse:	3✔
26	[anInteger = 1	3✔
27	ifTrue: [PMCauchyDistribution shape: 0 scale: 1]	3✔
28	ifFalse: [super new initialize: anInteger]]	3✔
29	]	3✔
30
31	{ #category : #information }
32	PMStudentDistribution class >> distributionName [	×
33		×
34	^'Student distribution'	×
35	]	×
36
37	{ #category : #creation }
38	PMStudentDistribution class >> fromHistogram: aHistogram [	×
39	"Create an instance of the receiver with parameters estimated from the given histogram using best guesses. This method can be used to find the initial values for a fit."	×
40	\| dof var \|	×
41	var := aHistogram variance.	×
42	var = 0	×
43	ifTrue: [ ^nil].	×
44	dof := ( 2 / (1 - (1 / aHistogram variance))) rounded max: 1.	×
45	^dof > self asymptoticLimit ifTrue: [ nil]	×
46	ifFalse:[ self degreeOfFreedom: dof]	×
47	]	×
48
49	{ #category : #creation }
50	PMStudentDistribution class >> new [	×
51		×
52	^self error: 'Illegal creation message for this class'	×
53	]	×
54
55	{ #category : #creation }
56	PMStudentDistribution class >> test: aStatisticalMoment1 with: aStatisticalMoment2 [	×
57	"Perform a consistency Student test (or t-test) on the averages of two statistical moments ( or histograms). Answers the probability of failing the test."	×
58	\| t \|	×
59	t := ( aStatisticalMoment1 average - aStatisticalMoment2 average) abs.	×
60	^1 - ( ( self class degreeOfFreedom: ( aStatisticalMoment1 count + aStatisticalMoment2 count - 2)) acceptanceBetween: t negated and: t)	×
61	]	×
62
63	{ #category : #information }
64	PMStudentDistribution >> average [	3✔
65		3✔
66	^0	3✔
67	]	3✔
68
69	{ #category : #transformation }
70	PMStudentDistribution >> changeParametersBy: aVector [	×
71	"Modify the parameters of the receiver by aVector."	×
72	degreeOfFreedom := degreeOfFreedom + ( aVector at: 1).	×
73	self computeNorm	×
74	]	×
75
76	{ #category : #information }
77	PMStudentDistribution >> chiSquareDistribution [	×
78	"Answer the chi square distribution used to generate random numbers for the receiver."	×
79		×
80	chiSquareDistribution ifNil: [ chiSquareDistribution := PMChiSquareDistribution degreeOfFreedom: degreeOfFreedom - 1 ].	×
81	^ chiSquareDistribution	×
82	]	×
83
84	{ #category : #private }
85	PMStudentDistribution >> computeNorm [	3✔
86	"Private - Compute the norm of the receiver because its parameters have changed."	3✔
87	norm := ( ( degreeOfFreedom / 2 logBeta: ( 1 / 2) ) + ( degreeOfFreedom ln / 2)) negated	3✔
88	]	3✔
89
90	{ #category : #information }
91	PMStudentDistribution >> confidenceLevel: aNumber [	3✔
92	"Answer the probability in percent of finding a value distributed according to the receiver with an absolute value larger than aNumber."	3✔
93	^( 1 - ( self symmetricAcceptance: aNumber abs)) * 100	3✔
94	]	3✔
95
96	{ #category : #information }
97	PMStudentDistribution >> distributionValue: aNumber [	3✔
98	"Answers the probability of observing a random variable distributed according to the receiver with a value lower than or equal to aNumber."	3✔
99	aNumber = 0	3✔
100	ifTrue: [ ^1/2].	3✔
101	^( aNumber > 0	3✔
102	ifTrue: [ 2 - ( self symmetricAcceptance: aNumber abs)]	3✔
103	ifFalse:[ self symmetricAcceptance: aNumber abs]) / 2	3✔
104	]	3✔
105
106	{ #category : #information }
107	PMStudentDistribution >> incompleteBetaFunction [	3✔
108	"Private - Answers the incomplete beta function used to compute the symmetric acceptance integral of the receiver."	3✔
109		3✔
110	incompleteBetaFunction ifNil: [ incompleteBetaFunction := PMIncompleteBetaFunction shape: degreeOfFreedom / 2 shape: 0.5 ].	3✔
111	^ incompleteBetaFunction	3✔
112	]	3✔
113
114	{ #category : #initialization }
115	PMStudentDistribution >> initialize: anInteger [	3✔
116		3✔
117	anInteger > 0	3✔
118	ifFalse: [ self error: 'Degree of freedom must be positive'].	3✔
119	degreeOfFreedom := anInteger.	3✔
120	self computeNorm.	3✔
121	^self	3✔
122	]	3✔
123
124	{ #category : #information }
125	PMStudentDistribution >> kurtosis [	×
126	"Answer the kurtosis of the receiver. Undefined if the degree of freedom is less than 5."	×
127	^degreeOfFreedom > 4 ifTrue: [ 6 / ( degreeOfFreedom - 4)]	×
128	ifFalse:[ nil]	×
129	]	×
130
131	{ #category : #information }
132	PMStudentDistribution >> parameters [	×
133		×
134	^Array with: degreeOfFreedom	×
135	]	×
136
137	{ #category : #information }
138	PMStudentDistribution >> random [	×
139	"Answer a random number distributed according to the receiver."	×
140	^PMNormalDistribution random * ( ( (degreeOfFreedom - 1) / self chiSquareDistribution random ) sqrt)	×
141	]	×
142
143	{ #category : #information }
144	PMStudentDistribution >> skewness [	×
145		×
146	^0	×
147	]	×
148
149	{ #category : #information }
150	PMStudentDistribution >> symmetricAcceptance: aNumber [	3✔
151	"Compute the acceptance of the receiver between -aNumber and aNumber"	3✔
152	^ self incompleteBetaFunction value: ( degreeOfFreedom / ( aNumber squared + degreeOfFreedom))	3✔
153	]	3✔
154
155	{ #category : #information }
156	PMStudentDistribution >> value: aNumber [	3✔
157	"Answers the probability that a random variable distributed according to the receiver gives a value between aNumber and aNumber + espilon (infinitesimal interval)."	3✔
158	^( norm - ( ( aNumber squared / degreeOfFreedom + 1) ln * ( ( degreeOfFreedom + 1) / 2))) exp	3✔
159	]	3✔
160
161	{ #category : #information }
162	PMStudentDistribution >> variance [	×
163	"Answer the variance of the receiver. Undefined if the degree of freedom is less than 3."	×
164	^degreeOfFreedom > 2	×
165	ifTrue: [ degreeOfFreedom / ( degreeOfFreedom - 2)]	×
166	ifFalse:[ nil]	×
167	]	×

PolyMathOrg / PolyMath / 4385132063

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