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TukeyLambdaDistribution
TukeyLambdaDistribution[
]
represents Tukey's lambda distribution with shape parameter .
TukeyLambdaDistribution[, 
, 
]
represents Tukey's lambda distribution with location parameter and scale parameter .
TukeyLambdaDistribution[{1, 2}, , {1, 2}]
represents the generalized Tukey's lambda distribution with location parameter , scale parameters 
and 
, and shape parameters 
and 
.
Details
- The quantile function for value
in a Tukey lambda distribution is equal to 
for 
and 
, and 
when 
. - TukeyLambdaDistribution[] is equivalent to TukeyLambdaDistribution[, 0, 1].
- The quantile function for value
in a generalized Tukey lambda distribution is equal to 
for 
. - TukeyLambdaDistribution allows ,
, 
, and to be any real numbers, and , 
, and 
any positive real numbers. - TukeyLambdaDistribution can be used with such functions as Mean, CDF, and RandomVariate.
Examplesopen all
Basic Examples (15)
Quantile function for symmetric case:
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Quantile function with location and scale parameters:
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Quantile function for generalized Tukey's lambda distribution:
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Probability density function does not have closed form but can be found numerically:
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Cumulative distribution function does not have closed form but can be found numerically:
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Mean and variance have closed forms:
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Probability density function with location and scale:
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Cumulative distribution function with location and scale:
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Mean and variance with location and scale:
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Median with location and scale:
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Probability density function of generalized Tukey lambda distribution:
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Cumulative distribution function of generalized Tukey lambda distribution:
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Mean and variance of generalized Tukey lambda distribution:
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Median of generalized Tukey lambda distribution:
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