Wald: Wald Distribution Class

Description

Mathematical and statistical functions for the Wald distribution, which is commonly used for modelling the first passage time for Brownian motion.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Wald$new(mean = 1, shape = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`mean`	numeric	location parameter.
`shape`	numeric	shape parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Wald distribution is parameterised with mean and shape as positive numerics.

Public Variables

Variable	Return
`name`	Name of distribution.
`short_name`	Id of distribution.
`description`	Brief description of distribution.

Public Methods

Accessor Methods	Link
`decorators()`	`decorators`
`traits()`	`traits`
`valueSupport()`	`valueSupport`
`variateForm()`	`variateForm`
`type()`	`type`
`properties()`	`properties`
`support()`	`support`
`symmetry()`	`symmetry`
`sup()`	`sup`
`inf()`	`inf`
`dmax()`	`dmax`
`dmin()`	`dmin`
`skewnessType()`	`skewnessType`
`kurtosisType()`	`kurtosisType`



Statistical Methods	Link
`pdf(x1, ..., log = FALSE, simplify = TRUE)`	`pdf`
`cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`cdf`
`quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`quantile.Distribution`
`rand(n, simplify = TRUE)`	`rand`
`mean()`	`mean.Distribution`
`variance()`	`variance`
`stdev()`	`stdev`
`prec()`	`prec`
`cor()`	`cor`
`skewness()`	`skewness`
`kurtosis(excess = TRUE)`	`kurtosis`
`entropy(base = 2)`	`entropy`
`mgf(t)`	`mgf`
`cf(t)`	`cf`
`pgf(z)`	`pgf`
`median()`	`median.Distribution`
`iqr()`	`iqr`



Parameter Methods	Link
`parameters(id)`	`parameters`
`getParameterValue(id, error = "warn")`	`getParameterValue`
`setParameterValue(..., lst = NULL, error = "warn")`	`setParameterValue`



Validation Methods	Link
`liesInSupport(x, all = TRUE, bound = FALSE)`	`liesInSupport`
`liesInType(x, all = TRUE, bound = FALSE)`	`liesInType`



Representation Methods	Link
`strprint(n = 2)`	`strprint`
`print(n = 2)`	`print`
`summary(full = T)`	`summary.Distribution`

Details

The Wald distribution parameterised with mean, $\mu$, and shape, $\lambda$, is defined by the pdf, $$f(x) = (\lambda/(2x^3\pi))^{1/2} exp((-\lambda(x-\mu)^2)/(2\mu^2x))$$ for $\lambda > 0$ and $\mu > 0$.

The distribution is supported on the Positive Reals.

entropy is omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results. quantile is omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.

Also known as the Inverse Normal distribution. Sampling is performed as per Michael, Schucany, Haas (1976).

References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

Michael, John R.; Schucany, William R.; Haas, Roy W. (May 1976). "Generating Random Variates Using Transformations with Multiple Roots". The American Statistician. 30 (2): 88<U+2013>90. doi:10.2307/2683801. JSTOR 2683801.

Examples

Run this code

# NOT RUN {
x = Wald$new(mean = 2, shape = 5)

# Update parameters
x$setParameterValue(shape = 3)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }

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