Pearson Type III Inverse CDF (Quantile Function)

Computes quantiles from a Pearson Type III distribution given probabilities and distribution parameters (mean, standard deviation, skewness).

Usage

qp3(p, mu, sigma, gamma)

Arguments

p: Vector of probabilities (between 0 and 1).
mu: Mean of the distribution.
sigma: Standard deviation of the distribution.
gamma: Skewness coefficient of the distribution.

Value

Vector of quantiles corresponding to the input probabilities.

Details

NOTE: This is the non-vectorized version of the function (it will be used in a loop) Vectorized version is part of future development.

The Pearson Type III distribution is parameterized by mean (mu), standard deviation (sigma), and skewness (gamma). These are converted internally to location, scale, and shape parameters.

When skewness is near zero (abs(gamma) < 1E-3), the normal distribution is used as an approximation.

Examples

# Single quantile
qp3(0.99, mu = 10, sigma = 2, gamma = 0.5)
#> [1] 15.37144

# Multiple quantiles
qp3(c(0.5, 0.9, 0.99), mu = 10, sigma = 2, gamma = 0.5)
#> [1]  9.833965 12.646186 15.371443

# Use with JMD volume-frequency parameters
qp3(0.99,
    mu = jmd_vfc_parameters$mean_log,
    sigma = jmd_vfc_parameters$sd_log,
    gamma = jmd_vfc_parameters$skew_log)
#> [1] 4.61417