sd_from_min_max: Distribution from minimum and maximum

In HelpersMG: Tools for Environmental Analyses, Ecotoxicology and Various R Functions

Distribution from minimum and maximum

Description

Bayesian estimate of underlying distribution.
The distribution of extrema is expected to be a Gaussian distribution; we could do better using generalized extreme value (GEV) distribution.
Weisstein, Eric W. "Extreme value distribution". mathworld.wolfram.com

Usage

sd_from_min_max(
  n,
  observedMean = NULL,
  observedMinimum,
  observedMaximum,
  priors = NULL,
  fittedparameters = c("mean-sd"),
  n.iter = 10000,
  n.chains = 1,
  n.adapt = 100,
  thin = 30,
  adaptive = FALSE,
  trace = 100
)

Arguments

n	Number of observations used to estimate observedMinimum and observedMaximum
observedMean	The observed mean (can be omited)
observedMinimum	The observed minimum
observedMaximum	The observed maximum
priors	The priors (can be omited)
fittedparameters	Can be "sd" or "mean-sd"
n.iter	Number of iterations for each chain
n.chains	Number of chains
n.adapt	Number of iteration to stabilize likelihood
thin	Interval for thinning likelihoods
adaptive	Should an adaptive process for SDProp be used
trace	Or FALSE or period to show progress

Details

sd_from_min_max returns standard deviation and/or mean from minimum and maximum

Value

sd_from_min_max returns a mcmcComposite object

Author(s)

Marc Girondot [e-mail]

Examples

## Not run: 
minobs <- 45
maxobs <- 53
n <- 4
# To estimate only the sd of the distribution
out_sd_mcmc <- sd_from_min_max(n=n, observedMinimum=minobs, 
                           observedMaximum=maxobs, 
                           fittedparameters="sd")
plot(out_sd_mcmc, what="MarkovChain", parameters="sd")
plot(out_sd_mcmc, what="posterior", parameters="sd")
as.parameters(out_sd_mcmc, index="quantile")
# To be compared with the rule of thumb:
print(paste0("sd = ", as.character((maxobs - minobs) / 4))) # SD Clearly biased

# To estimate both the sd and mean of the distribution

out_sd_mean_mcmc <- sd_from_min_max(n=n, observedMinimum=minobs, 
                           observedMaximum=maxobs, 
                           fittedparameters="mean-sd")

plot(out_sd_mean_mcmc, what="MarkovChain", parameters="sd")
plot(out_sd_mean_mcmc, what="MarkovChain", parameters="mean")
plot(out_sd_mean_mcmc, what="posterior", parameters="mean", xlim=c(0, 100), 
     breaks=seq(from=0, to=100, by=5))
as.parameters(out_sd_mean_mcmc, index="quantile")
# To be compared with the rule of thumb:
print(paste0("mean = ", as.character((maxobs + minobs) / 2))) # Mean Not so bad
print(paste0("sd = ", as.character((maxobs - minobs) / 4))) # SD Clearly biased

# Covariation of sd and mean is nearly NULL
cor(x=as.parameters(out_sd_mean_mcmc, index="all")[, "mean"], 
    y=as.parameters(out_sd_mean_mcmc, index="all")[, "sd"])^2
plot(x=as.parameters(out_sd_mean_mcmc, index="all")[, "mean"], 
     y=as.parameters(out_sd_mean_mcmc, index="all")[, "sd"], 
     xlab="mean", ylab="sd")



## End(Not run)

HelpersMG documentation built on June 8, 2025, 12:11 p.m.