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* @license Apache-2.0
*
* Copyright (c) 2026 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.
*/
/* eslint-disable no-restricted-syntax, no-invalid-this */
'use strict';
// MODULES //
var defineProperty = require( '@stdlib/utils/define-property' );
var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
var setReadOnlyAccessor = require( '@stdlib/utils/define-nonenumerable-read-only-accessor' );
var isPositive = require( '@stdlib/assert/is-positive-number' ).isPrimitive;
var kurtosis = require( '@stdlib/stats/base/dists/wald/kurtosis' );
var mean = require( '@stdlib/stats/base/dists/wald/mean' );
var mode = require( '@stdlib/stats/base/dists/wald/mode' );
var skewness = require( '@stdlib/stats/base/dists/wald/skewness' );
var stdev = require( '@stdlib/stats/base/dists/wald/stdev' );
var variance = require( '@stdlib/stats/base/dists/wald/variance' );
var cdf = require( '@stdlib/stats/base/dists/wald/cdf' );
var logcdf = require( '@stdlib/stats/base/dists/wald/logcdf' );
var logpdf = require( '@stdlib/stats/base/dists/wald/logpdf' );
var mgf = require( '@stdlib/stats/base/dists/wald/mgf' );
var pdf = require( '@stdlib/stats/base/dists/wald/pdf' );
var quantile = require( '@stdlib/stats/base/dists/wald/quantile' );
var format = require( '@stdlib/string/format' );
// FUNCTIONS //
/**
* Evaluates the cumulative distribution function (CDF).
*
* @private
* @param {number} x - input value
* @returns {Probability} evaluated CDF
*/
function waldCDF( x ) {
return cdf( x, this.mu, this.lambda );
}
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF).
*
* @private
* @param {number} x - input value
* @returns {number} evaluated logCDF
*/
function waldLogCDF( x ) {
return logcdf( x, this.mu, this.lambda );
}
/**
* Evaluates the natural logarithm of the probability density function (PDF).
*
* @private
* @param {number} x - input value
* @returns {number} evaluated logPDF
*/
function waldLogPDF( x ) {
return logpdf( x, this.mu, this.lambda );
}
/**
* Evaluates the moment-generating function (MGF).
*
* @private
* @param {number} t - input value
* @returns {number} evaluated MGF
*/
function waldMGF( t ) {
return mgf( t, this.mu, this.lambda );
}
/**
* Evaluates the probability density function (PDF).
*
* @private
* @param {number} x - input value
* @returns {number} evaluated PDF
*/
function waldPDF( x ) {
return pdf( x, this.mu, this.lambda );
}
/**
* Evaluates the quantile function.
*
* @private
* @param {Probability} p - input probability
* @returns {number} evaluated quantile function
*/
function waldQuantile( p ) {
return quantile( p, this.mu, this.lambda );
}
// MAIN //
/**
* Wald distribution constructor.
*
* @constructor
* @param {PositiveNumber} [mu=1.0] - mean
* @param {PositiveNumber} [lambda=1.0] - shape parameter
* @throws {TypeError} `mu` must be a positive number
* @throws {TypeError} `lambda` must be a positive number
* @returns {Wald} distribution instance
*
* @example
* var wald = new Wald( 1.0, 1.0 );
*
* var y = wald.cdf( 1.5 );
* // returns ~0.811
*
* var mu = wald.mean;
* // returns 1.0
*/
function Wald() {
var lambda;
var mu;
if ( !(this instanceof Wald) ) {
if ( arguments.length === 0 ) {
return new Wald();
}
return new Wald( arguments[ 0 ], arguments[ 1 ] );
}
if ( arguments.length ) {
mu = arguments[ 0 ];
lambda = arguments[ 1 ];
if ( !isPositive( mu ) ) {
throw new TypeError( format( 'invalid argument. Mean parameter must be a positive number. Value: `%s`.', mu ) );
}
if ( !isPositive( lambda ) ) {
throw new TypeError( format( 'invalid argument. Shape parameter must be a positive number. Value: `%s`.', lambda ) );
}
} else {
mu = 1.0;
lambda = 1.0;
}
defineProperty( this, 'mu', {
'configurable': false,
'enumerable': true,
'get': function get() {
return mu;
},
'set': function set( value ) {
if ( !isPositive( value ) ) {
throw new TypeError( format( 'invalid assignment. Must be a positive number. Value: `%s`.', value ) );
}
mu = value;
}
});
defineProperty( this, 'lambda', {
'configurable': false,
'enumerable': true,
'get': function get() {
return lambda;
},
'set': function set( value ) {
if ( !isPositive( value ) ) {
throw new TypeError( format( 'invalid assignment. Must be a positive number. Value: `%s`.', value ) );
}
lambda = value;
}
});
return this;
}
/**
* Wald distribution excess kurtosis.
*
* @name kurtosis
* @memberof Wald.prototype
* @type {number}
* @see [kurtosis]{@link https://en.wikipedia.org/wiki/Kurtosis}
*
* @example
* var wald = new Wald( 4.0, 12.0 );
*
* var v = wald.kurtosis;
* // returns 5.0
*/
setReadOnlyAccessor( Wald.prototype, 'kurtosis', function get() {
return kurtosis( this.mu, this.lambda );
});
/**
* Wald distribution expected value.
*
* @name mean
* @memberof Wald.prototype
* @type {number}
* @see [expected value]{@link https://en.wikipedia.org/wiki/Expected_value}
*
* @example
* var wald = new Wald( 4.0, 12.0 );
*
* var v = wald.mean;
* // returns 4.0
*/
setReadOnlyAccessor( Wald.prototype, 'mean', function get() {
return mean( this.mu, this.lambda );
});
/**
* Wald distribution mode.
*
* @name mode
* @memberof Wald.prototype
* @type {number}
* @see [mode]{@link https://en.wikipedia.org/wiki/Mode_%28statistics%29}
*
* @example
* var wald = new Wald( 4.0, 12.0 );
*
* var v = wald.mode;
* // returns ~2.472
*/
setReadOnlyAccessor( Wald.prototype, 'mode', function get() {
return mode( this.mu, this.lambda );
});
/**
* Wald distribution skewness.
*
* @name skewness
* @memberof Wald.prototype
* @type {number}
* @see [skewness]{@link https://en.wikipedia.org/wiki/Skewness}
*
* @example
* var wald = new Wald( 4.0, 12.0 );
*
* var v = wald.skewness;
* // returns ~1.732
*/
setReadOnlyAccessor( Wald.prototype, 'skewness', function get() {
return skewness( this.mu, this.lambda );
});
/**
* Wald distribution standard deviation.
*
* @name stdev
* @memberof Wald.prototype
* @type {PositiveNumber}
* @see [standard deviation]{@link https://en.wikipedia.org/wiki/Standard_deviation}
*
* @example
* var wald = new Wald( 4.0, 12.0 );
*
* var v = wald.stdev;
* // returns ~2.309
*/
setReadOnlyAccessor( Wald.prototype, 'stdev', function get() {
return stdev( this.mu, this.lambda );
});
/**
* Wald distribution variance.
*
* @name variance
* @memberof Wald.prototype
* @type {PositiveNumber}
* @see [variance]{@link https://en.wikipedia.org/wiki/Variance}
*
* @example
* var wald = new Wald( 4.0, 12.0 );
*
* var v = wald.variance;
* // returns ~5.333
*/
setReadOnlyAccessor( Wald.prototype, 'variance', function get() {
return variance( this.mu, this.lambda );
});
/**
* Evaluates the cumulative distribution function (CDF).
*
* @name cdf
* @memberof Wald.prototype
* @type {Function}
* @param {number} x - input value
* @returns {number} evaluated CDF
* @see [cdf]{@link https://en.wikipedia.org/wiki/Cumulative_distribution_function}
*
* @example
* var wald = new Wald( 2.0, 4.0 );
*
* var v = wald.cdf( 0.5 );
* // returns ~0.028
*/
setReadOnly( Wald.prototype, 'cdf', waldCDF );
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF).
*
* @name logcdf
* @memberof Wald.prototype
* @type {Function}
* @param {number} x - input value
* @returns {number} evaluated logarithm of the CDF
* @see [cdf]{@link https://en.wikipedia.org/wiki/Cumulative_distribution_function}
*
* @example
* var wald = new Wald( 2.0, 4.0 );
*
* var v = wald.logcdf( 0.5 );
* // returns ~-3.574
*/
setReadOnly( Wald.prototype, 'logcdf', waldLogCDF );
/**
* Evaluates the natural logarithm of the probability density function (PDF).
*
* @name logpdf
* @memberof Wald.prototype
* @type {Function}
* @param {number} x - input value
* @returns {number} evaluated logPDF
* @see [pdf]{@link https://en.wikipedia.org/wiki/Probability_density_function}
*
* @example
* var wald = new Wald( 2.0, 4.0 );
*
* var v = wald.logpdf( 0.8 );
* // returns ~-0.791
*/
setReadOnly( Wald.prototype, 'logpdf', waldLogPDF );
/**
* Evaluates the moment-generating function (MGF).
*
* @name mgf
* @memberof Wald.prototype
* @type {Function}
* @param {number} t - input value
* @returns {number} evaluated MGF
* @see [mgf]{@link https://en.wikipedia.org/wiki/Moment-generating_function}
*
* @example
* var wald = new Wald( 2.0, 4.0 );
*
* var v = wald.mgf( 0.01 );
* // returns ~1.02
*/
setReadOnly( Wald.prototype, 'mgf', waldMGF );
/**
* Evaluates the probability density function (PDF).
*
* @name pdf
* @memberof Wald.prototype
* @type {Function}
* @param {number} x - input value
* @returns {number} evaluated PDF
* @see [pdf]{@link https://en.wikipedia.org/wiki/Probability_density_function}
*
* @example
* var wald = new Wald( 2.0, 4.0 );
*
* var v = wald.pdf( 0.8 );
* // returns ~0.453
*/
setReadOnly( Wald.prototype, 'pdf', waldPDF );
/**
* Evaluates the quantile function.
*
* @name quantile
* @memberof Wald.prototype
* @type {Function}
* @param {Probability} p - input probability
* @returns {number} evaluated quantile function
* @see [quantile function]{@link https://en.wikipedia.org/wiki/Quantile_function}
*
* @example
* var wald = new Wald( 2.0, 4.0 );
*
* var v = wald.quantile( 0.5 );
* // returns ~1.609
*/
setReadOnly( Wald.prototype, 'quantile', waldQuantile );
// EXPORTS //
module.exports = Wald;
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