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index.d.ts
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index.d.ts
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/*
* @license Apache-2.0
*
* Copyright (c) 2019 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
// TypeScript Version: 2.0
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Pareto (Type I) distribution.
*
* @param x - input value
* @returns evaluated logCDF
*/
type Unary = ( x: number ) => number;
/**
* Interface for the logarithm of the cumulative distribution function (CDF) of a Pareto (Type I) distribution.
*/
interface LogCDF {
/**
* Evaluates the cumulative distribution function (CDF) for a Pareto (Type I) distribution with shape parameter `alpha` and scale parameter `beta` at a value `x`.
*
* ## Notes
*
* - If `alpha <= 0` or `beta <= 0`, the function returns `NaN`.
*
* @param x - input value
* @param alpha - shape parameter
* @param beta - scale parameter
* @returns evaluated logCDF
*
* @example
* var y = logcdf( 2.0, 1.0, 1.0 );
* // returns ~-0.693
*
* @example
* var y = logcdf( 5.0, 2.0, 4.0 );
* // returns ~-1.022
*
* @example
* var y = logcdf( 4.0, 2.0, 2.0 );
* // returns ~-0.288
*
* @example
* var y = logcdf( 1.9, 2.0, 2.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( +Infinity, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = logcdf( 2.0, -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = logcdf( 2.0, 0.5, -1.0 );
* // returns NaN
*
* @example
* var y = logcdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, 1.0, NaN );
* // returns NaN
*/
( x: number, alpha: number, beta: number ): number;
/**
* Returns a function for evaluating the natural logarithm of the cumulative distribution function (CDF) for a Pareto (Type I) distribution with shape parameter `alpha` and scale parameter `beta`.
*
* @param alpha - shape parameter
* @param beta - scale parameter
* @returns logCDF
*
* @example
* var mylogcdf = logcdf.factory( 10.0, 2.0 );
* var y = mylogcdf( 3.0 );
* // returns ~-0.017
*
* y = mylogcdf( 2.5 );
* // returns ~-0.114
*/
factory( alpha: number, beta: number ): Unary;
}
/**
* Pareto (Type I) distribution logarithm of cumulative distribution function (CDF).
*
* @param x - input value
* @param alpha - shape parameter
* @param beta - scale parameter
* @returns evaluated logCDF
*
* @example
* var y = logcdf( 2.0, 1.0, 1.0 );
* // returns ~-0.693
*
* y = logcdf( 5.0, 2.0, 4.0 );
* // returns ~-1.022
*
* y = logcdf( 4.0, 2.0, 2.0 );
* // returns ~-0.288
*
* y = logcdf( 1.9, 2.0, 2.0 );
* // returns -Infinity
*
* y = logcdf( +Infinity, 4.0, 2.0 );
* // returns 0.0
*
* var mylogcdf = logcdf.factory( 10.0, 2.0 );
* y = mylogcdf( 3.0 );
* // returns ~-0.017
*
* y = mylogcdf( 2.5 );
* // returns ~-0.113
*/
declare var logCDF: LogCDF;
// EXPORTS //
export = logCDF;