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base.dists.lognormal.entropy,"\nbase.dists.lognormal.entropy( μ, σ )\n Returns the differential entropy of a lognormal distribution with location\n `μ` and scale `σ` (in nats).\n\n If provided `NaN` as any argument, the function returns `NaN`.\n\n If provided `σ <= 0`, the function returns `NaN`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n out: number\n Entropy.\n\n Examples\n --------\n > var y = base.dists.lognormal.entropy( 0.0, 1.0 )\n ~1.419\n > y = base.dists.lognormal.entropy( 5.0, 2.0 )\n ~7.112\n > y = base.dists.lognormal.entropy( NaN, 1.0 )\n NaN\n > y = base.dists.lognormal.entropy( 0.0, NaN )\n NaN\n > y = base.dists.lognormal.entropy( 0.0, 0.0 )\n NaN\n\n"
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base.dists.lognormal.kurtosis,"\nbase.dists.lognormal.kurtosis( μ, σ )\n Returns the excess kurtosis of a lognormal distribution with location `μ`\n and scale `σ`.\n\n If provided `NaN` as any argument, the function returns `NaN`.\n\n If provided `σ <= 0`, the function returns `NaN`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n out: number\n Kurtosis.\n\n Examples\n --------\n > var y = base.dists.lognormal.kurtosis( 0.0, 1.0 )\n ~110.936\n > y = base.dists.lognormal.kurtosis( 5.0, 2.0 )\n ~9220556.977\n > y = base.dists.lognormal.kurtosis( NaN, 1.0 )\n NaN\n > y = base.dists.lognormal.kurtosis( 0.0, NaN )\n NaN\n > y = base.dists.lognormal.kurtosis( 0.0, 0.0 )\n NaN\n\n"
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base.dists.lognormal.LogNormal,"\nbase.dists.lognormal.LogNormal( [μ, σ] )\n Returns a lognormal distribution object.\n\n Parameters\n ----------\n μ: number (optional)\n Location parameter. Default: `0.0`.\n\n σ: number (optional)\n Scale parameter. Must be greater than `0`. Default: `1.0`.\n\n Returns\n -------\n lognormal: Object\n Distribution instance.\n\n lognormal.mu: number\n Location parameter.\n\n lognormal.sigma: number\n Scale parameter. If set, the value must be greater than `0`.\n\n lognormal.entropy: number\n Read-only property which returns the differential entropy.\n\n lognormal.kurtosis: number\n Read-only property which returns the excess kurtosis.\n\n lognormal.mean: number\n Read-only property which returns the expected value.\n\n lognormal.median: number\n Read-only property which returns the median.\n\n lognormal.mode: number\n Read-only property which returns the mode.\n\n lognormal.skewness: number\n Read-only property which returns the skewness.\n\n lognormal.stdev: number\n Read-only property which returns the standard deviation.\n\n lognormal.variance: number\n Read-only property which returns the variance.\n\n lognormal.cdf: Function\n Evaluates the cumulative distribution function (CDF).\n\n lognormal.logcdf: Function\n Evaluates the natural logarithm of the cumulative distribution function\n (CDF).\n\n lognormal.logpdf: Function\n Evaluates the natural logarithm of the probability density function\n (PDF).\n\n lognormal.pdf: Function\n Evaluates the probability density function (PDF).\n\n lognormal.quantile: Function\n Evaluates the quantile function at probability `p`.\n\n Examples\n --------\n > var lognormal = base.dists.lognormal.LogNormal( -2.0, 3.0 );\n > lognormal.mu\n -2.0\n > lognormal.sigma\n 3.0\n > lognormal.entropy\n ~0.518\n > lognormal.kurtosis\n 4312295840576300\n > lognormal.mean\n ~12.182\n > lognormal.median\n ~0.135\n > lognormal.mode\n ~0.0\n > lognormal.skewness\n ~729551.383\n > lognormal.stdev\n ~1096.565\n > lognormal.variance\n ~1202455.871\n > lognormal.cdf( 0.8 )\n ~0.723\n > lognormal.logcdf( 0.8 )\n ~-4.334\n > lognormal.logpdf( 2.0 )\n ~-3.114\n > lognormal.pdf( 2.0 )\n ~0.044\n > lognormal.quantile( 0.9 )\n ~6.326\n\n"
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base.dists.lognormal.logcdf,"\nbase.dists.lognormal.logcdf( x, μ, σ )\n Evaluates the natural logarithm of the cumulative distribution function\n (CDF) for a lognormal distribution with mean `μ` and standard deviation `σ`\n at a value `x`.\n\n If provided `NaN` as any argument, the function returns `NaN`.\n\n If provided `σ < 0`, the function returns `NaN`.\n\n Parameters\n ----------\n x: number\n Input value.\n\n μ: number\n Location parameter.\n\n σ: number\n Standard deviation.\n\n Returns\n -------\n out: number\n Evaluated logcdf.\n\n Examples\n --------\n > var y = base.dists.lognormal.logcdf( 2.0, 0.0, 1.0 )\n ~-0.2799\n > y = base.dists.lognormal.logcdf( 13.0, 4.0, 2.0 )\n ~-1.442\n > y = base.dists.lognormal.logcdf( NaN, 0.0, 1.0 )\n NaN\n > y = base.dists.lognormal.logcdf( 0.0, NaN, 1.0 )\n NaN\n > y = base.dists.lognormal.logcdf( 0.0, 0.0, NaN )\n NaN\n\n // Negative standard deviation:\n > y = base.dists.lognormal.logcdf( 2.0, 0.0, -1.0 )\n NaN\n\n // Degenerate distribution centered at `μ` when `σ = 0.0`:\n > y = base.dists.lognormal.logcdf( 2.0, 8.0, 0.0 )\n -Infinity\n > y = base.dists.lognormal.logcdf( 8.0, 8.0, 0.0 )\n -Infinity\n\n\nbase.dists.lognormal.logcdf.factory( μ, σ )\n Returns a function for evaluating the natural logarithm of the cumulative\n distribution function (CDF) of a lognormal distribution with mean `μ` and\n standard deviation `σ`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Standard deviation.\n\n Returns\n -------\n logcdf: Function\n Logarithm of cumulative distribution function (CDF).\n\n Examples\n --------\n > var mylogcdf = base.dists.lognormal.logcdf.factory( 10.0, 2.0 );\n > var y = mylogcdf( 10.0 )\n ~-9.732\n\n"
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base.dists.lognormal.logcdf.factory,"\nbase.dists.lognormal.logcdf.factory( μ, σ )\n Returns a function for evaluating the natural logarithm of the cumulative\n distribution function (CDF) of a lognormal distribution with mean `μ` and\n standard deviation `σ`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Standard deviation.\n\n Returns\n -------\n logcdf: Function\n Logarithm of cumulative distribution function (CDF).\n\n Examples\n --------\n > var mylogcdf = base.dists.lognormal.logcdf.factory( 10.0, 2.0 );\n > var y = mylogcdf( 10.0 )\n ~-9.732"
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base.dists.lognormal.logcdf,"\nbase.dists.lognormal.logcdf( x, μ, σ )\n Evaluates the natural logarithm of the cumulative distribution function\n (CDF) for a lognormal distribution with location parameter `μ` and scale\n parameter `σ` at a value `x`.\n\n If provided `NaN` as any argument, the function returns `NaN`.\n\n If provided `σ < 0`, the function returns `NaN`.\n\n Parameters\n ----------\n x: number\n Input value.\n\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n out: number\n Evaluated logcdf.\n\n Examples\n --------\n > var y = base.dists.lognormal.logcdf( 2.0, 0.0, 1.0 )\n ~-0.2799\n > y = base.dists.lognormal.logcdf( 13.0, 4.0, 2.0 )\n ~-1.442\n > y = base.dists.lognormal.logcdf( NaN, 0.0, 1.0 )\n NaN\n > y = base.dists.lognormal.logcdf( 0.0, NaN, 1.0 )\n NaN\n > y = base.dists.lognormal.logcdf( 0.0, 0.0, NaN )\n NaN\n\n // Negative scale parameter:\n > y = base.dists.lognormal.logcdf( 2.0, 0.0, -1.0 )\n NaN\n\n // Degenerate distribution centered at `μ` when `σ = 0.0`:\n > y = base.dists.lognormal.logcdf( 2.0, 8.0, 0.0 )\n -Infinity\n > y = base.dists.lognormal.logcdf( 8.0, 8.0, 0.0 )\n -Infinity\n\n\nbase.dists.lognormal.logcdf.factory( μ, σ )\n Returns a function for evaluating the natural logarithm of the cumulative\n distribution function (CDF) of a lognormal distribution with location\n parameter `μ` and scale parameter `σ`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n logcdf: Function\n Logarithm of cumulative distribution function (CDF).\n\n Examples\n --------\n > var mylogcdf = base.dists.lognormal.logcdf.factory( 10.0, 2.0 );\n > var y = mylogcdf( 10.0 )\n ~-9.732\n\n"
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base.dists.lognormal.logcdf.factory,"\nbase.dists.lognormal.logcdf.factory( μ, σ )\n Returns a function for evaluating the natural logarithm of the cumulative\n distribution function (CDF) of a lognormal distribution with location\n parameter `μ` and scale parameter `σ`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n logcdf: Function\n Logarithm of cumulative distribution function (CDF).\n\n Examples\n --------\n > var mylogcdf = base.dists.lognormal.logcdf.factory( 10.0, 2.0 );\n > var y = mylogcdf( 10.0 )\n ~-9.732"
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base.dists.lognormal.logpdf,"\nbase.dists.lognormal.logpdf( x, μ, σ )\n Evaluates the natural logarithm of the probability density function (PDF)\n for a lognormal distribution with location parameter `μ` and scale parameter\n `σ` at a value `x`.\n\n If provided `NaN` as any argument, the function returns `NaN`.\n\n If provided `σ <= 0`, the function returns `NaN`.\n\n Parameters\n ----------\n x: number\n Input value.\n\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n out: number\n Evaluated logPDF.\n\n Examples\n --------\n > var y = base.dists.lognormal.logpdf( 2.0, 0.0, 1.0 )\n ~-1.852\n > y = base.dists.lognormal.logpdf( 1.0, 0.0, 1.0 )\n ~-0.919\n > y = base.dists.lognormal.logpdf( 1.0, 3.0, 1.0 )\n ~-5.419\n > y = base.dists.lognormal.logpdf( -1.0, 4.0, 2.0 )\n -Infinity\n\n > y = base.dists.lognormal.logpdf( NaN, 0.0, 1.0 )\n NaN\n > y = base.dists.lognormal.logpdf( 0.0, NaN, 1.0 )\n NaN\n > y = base.dists.lognormal.logpdf( 0.0, 0.0, NaN )\n NaN\n\n // Non-positive scale parameter `σ`:\n > y = base.dists.lognormal.logpdf( 2.0, 0.0, -1.0 )\n NaN\n > y = base.dists.lognormal.logpdf( 2.0, 0.0, 0.0 )\n NaN\n\n\nbase.dists.lognormal.logpdf.factory( μ, σ )\n Returns a function for evaluating the natural logarithm of the probability\n density function (PDF) of a lognormal distribution with location parameter\n `μ` and scale parameter `σ`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n logpdf: Function\n Logarithm of probability density function (PDF).\n\n Examples\n --------\n > var mylogPDF = base.dists.lognormal.logpdf.factory( 4.0, 2.0 );\n > var y = mylogPDF( 10.0 )\n ~-4.275\n > y = mylogPDF( 2.0 )\n ~-3.672\n\n"
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base.dists.lognormal.logpdf.factory,"\nbase.dists.lognormal.logpdf.factory( μ, σ )\n Returns a function for evaluating the natural logarithm of the probability\n density function (PDF) of a lognormal distribution with location parameter\n `μ` and scale parameter `σ`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n logpdf: Function\n Logarithm of probability density function (PDF).\n\n Examples\n --------\n > var mylogPDF = base.dists.lognormal.logpdf.factory( 4.0, 2.0 );\n > var y = mylogPDF( 10.0 )\n ~-4.275\n > y = mylogPDF( 2.0 )\n ~-3.672"
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base.dists.lognormal.mean,"\nbase.dists.lognormal.mean( μ, σ )\n Returns the expected value of a lognormal distribution with location `μ` and\n scale `σ`.\n\n If provided `NaN` as any argument, the function returns `NaN`.\n\n If provided `σ <= 0`, the function returns `NaN`.\n\n Parameters\n ----------\n μ: number\n Location parameter.\n\n σ: number\n Scale parameter.\n\n Returns\n -------\n out: number\n Expected value.\n\n Examples\n --------\n > var y = base.dists.lognormal.mean( 0.0, 1.0 )\n ~1.649\n > y = base.dists.lognormal.mean( 4.0, 2.0 )\n ~403.429\n > y = base.dists.lognormal.mean( NaN, 1.0 )\n NaN\n > y = base.dists.lognormal.mean( 0.0, NaN )\n NaN\n > y = base.dists.lognormal.mean( 0.0, 0.0 )\n NaN\n\n"
base.dists.lognormal.entropy,"\nbase.dists.lognormal.entropy( μ:number, σ:number )\n Returns the differential entropy of a lognormal distribution with location\n `μ` and scale `σ` (in nats).\n"
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base.dists.lognormal.kurtosis,"\nbase.dists.lognormal.kurtosis( μ:number, σ:number )\n Returns the excess kurtosis of a lognormal distribution with location `μ`\n and scale `σ`.\n"
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base.dists.lognormal.LogNormal,"\nbase.dists.lognormal.LogNormal( [μ:number, σ:number] )\n Returns a lognormal distribution object.\n"
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base.dists.lognormal.logcdf,"\nbase.dists.lognormal.logcdf( x:number, μ:number, σ:number )\n Evaluates the natural logarithm of the cumulative distribution function\n (CDF) for a lognormal distribution with mean `μ` and standard deviation `σ`\n at a value `x`.\n"
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base.dists.lognormal.logcdf.factory,"\nbase.dists.lognormal.logcdf.factory( μ:number, σ:number )\n Returns a function for evaluating the natural logarithm of the cumulative\n distribution function (CDF) of a lognormal distribution with mean `μ` and\n standard deviation `σ`.\n"
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base.dists.lognormal.logcdf,"\nbase.dists.lognormal.logcdf( x:number, μ:number, σ:number )\n Evaluates the natural logarithm of the cumulative distribution function\n (CDF) for a lognormal distribution with location parameter `μ` and scale\n parameter `σ` at a value `x`.\n"
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base.dists.lognormal.logcdf.factory,"\nbase.dists.lognormal.logcdf.factory( μ:number, σ:number )\n Returns a function for evaluating the natural logarithm of the cumulative\n distribution function (CDF) of a lognormal distribution with location\n parameter `μ` and scale parameter `σ`.\n"
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base.dists.lognormal.logpdf,"\nbase.dists.lognormal.logpdf( x:number, μ:number, σ:number )\n Evaluates the natural logarithm of the probability density function (PDF)\n for a lognormal distribution with location parameter `μ` and scale parameter\n `σ` at a value `x`.\n"
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base.dists.lognormal.logpdf.factory,"\nbase.dists.lognormal.logpdf.factory( μ:number, σ:number )\n Returns a function for evaluating the natural logarithm of the probability\n density function (PDF) of a lognormal distribution with location parameter\n `μ` and scale parameter `σ`.\n"
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base.dists.lognormal.mean,"\nbase.dists.lognormal.mean( μ:number, σ:number )\n Returns the expected value of a lognormal distribution with location `μ` and\n scale `σ`.\n"
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