Foundation of MaxEnt and MinxEnt Distributions

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Foundation of MaxEnt and MinxEnt Distributions

• Senay ASMA
• Anadolu University, TURKEY
• Department of Statistics
• senayyolacan_at_anadolu.edu.tr

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Outline
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MaxEnt Distribution for Discrete Random
Variables
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MaxEnt Distribution for Continuous Random
Variables
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MinxEnt Distribution for Discrete Random
Variable
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MinxEnt Distribution for Continuous Random
Variable
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Relation between MaxEnt and MinxEnt
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EXAMPLES
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Example 1
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Solution
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Example 2
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Solution

• gt MinxEnt2(c(0,0))
• Langrangians
• 1 0.4460205 -0.1015608
• Estimates
• 0.03543016 0.07843508 0.13022935 0.19220067
  0.23402102 0.32968372

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Example 3
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Solution
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Relation between MaxEnt distributions and the
statistical probability distributions
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Illustrations
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Normal Dist. as MaxEnt Dist.
Langrangians 12.1368643 -2.5737688 0.1225747
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Cauchy Dist. as MaxEnt Dist.
Langrangians - 42.688153 1.999932
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Recommendation
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Problem
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m3 constraints
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m4 constraints
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m6 constraints
Langrangians 248.582864 -112.084654
2.674185 303.093256 157.269137 -199.529637
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Cassie Data
Langrangians - 0.9237672498 0.1028831364
0.0003409807 - 1.6859986648 - 0.5014575645
1.4025794790
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References
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A theorem for initial point problems