Parameterize a Three-Parameter Lognormal PMF for Stage

Computes the parameters of a three-parameter lognormal distribution for use as a probabilistic maximum stage (PMF) in rejection sampling. The shift parameter defines the lower or upper bound of the distribution (typically, the lower value). The function supports two modes: (1) supplying a best estimate and assuming sigma, or (2) supplying a best estimate, low, and high to solve for sigma numerically.

Usage

pmf_stage_lognormal(
  pmf_shift,
  pmf_mean,
  pmf_sigma = NULL,
  pmf_low = NULL,
  pmf_high = NULL
)

Arguments

pmf_shift

Numeric. Assumed lower-bound of the lognormal distribution. This will define the shift value. Must be less than all of pmf_mean, pmf_low, and pmf_high.

pmf_mean

Numeric. Assumed mean of the shifted PMF stage distribution.

pmf_sigma

Numeric. Assumed standard deviation on the log scale. Required if pmf_low and pmf_high are not supplied. Defaults to NULL. Suggested value = 0.5.

pmf_low

Numeric. Low estimate of PMF stage (assumed 5th percentile). Optional. If supplied, pmf_high must also be supplied.

pmf_high

Numeric. High estimate of PMF stage (assumed 95th percentile). Optional. If supplied, pmf_low must also be supplied.

Value

A named list with the following elements:

pmf_shift

Hard lower bound of the distribution.

pmf_mean

Assumed mean of shifted PMF stage distribution.

pmf_sigma

Standard deviation on the log scale.

pmf_mu

Derived location parameter on the log scale.

pmf_p05

5th percentile of the PMF stage distribution.

pmf_p95

95th percentile of the PMF stage distribution.

Examples

# Mode 1: assume sigma
pmf <- pmf_stage_lognormal(pmf_shift = 239, pmf_mean = 241.9, pmf_sigma = 0.5)

# Mode 2: solve for sigma from low/high estimates
pmf <- pmf_stage_lognormal(pmf_shift = 239, pmf_mean = 241.9,
                            pmf_low = 239, pmf_high = 245)