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BUILT-IN MATHEMATICA SYMBOL
WaringYuleDistribution
WaringYuleDistribution[
]
represents the Yule distribution with shape parameter .
WaringYuleDistribution[, 
]
represents the Waring distribution with shape parameters and .
Details
- WaringYuleDistribution[] is also known as the Yule-Simon distribution.
- The probability for integer value
in a Waring-Yule distribution is proportional to: -
WaringYuleDistribution[ ]![(TemplateBox[{{k, +, 1}}, Gamma])/(TemplateBox[{{k, +, alpha, +, 2}}, Gamma])](Files/WaringYuleDistribution.en/2.png "(TemplateBox[{{k, +, 1}}, Gamma])/(TemplateBox[{{k, +, alpha, +, 2}}, Gamma])")
WaringYuleDistribution[ , ]![(TemplateBox[{{k, +, beta}}, Gamma])/(TemplateBox[{{k, +, alpha, +, beta, +, 1}}, Gamma])](Files/WaringYuleDistribution.en/3.png "(TemplateBox[{{k, +, beta}}, Gamma])/(TemplateBox[{{k, +, alpha, +, beta, +, 1}}, Gamma])")
- WaringYuleDistribution allows and
to be any positive real numbers. - WaringYuleDistribution can be used with such functions as Mean, CDF, and RandomVariate.
Examplesopen all
Basic Examples (6)
Probability density function of Yule distribution:
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Cumulative distribution function of Yule distribution:
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Mean and variance of Yule distribution:
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Probability density function of Waring distribution:
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Cumulative distribution function of Waring distribution:
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Mean and variance of Waring distribution:
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