sim_sam_int: Simulated confidence interval of a statistic

In MOM: Estimation and Testing of Hypothesis

Simulated confidence interval of a statistic

Description

A function that returns a sampling interval for a statistic formed from random sample of certain probability distributions. The function generates the confidence interval using Monte Carlo simulations. The results might be unreliable if the resulting statistic has fat tailed distribution.

Usage

sim_sam_int(
  dist = c("normal", "lognormal", "gamma", "chisquare", "cauchy", "pareto", "weibull",
    "rayleigh", "laplace", "beta", "binomial", "poisson", "negativebinomial",
    "geometric", "t", "f", "uniform"),
  pop.par,
  FUN,
  side = c("lower", "upper", "both"),
  conf.coeff = 0.95,
  range = 1,
  n = 100,
  sim.size = 1000
)

Arguments

dist	The parent population distribution
pop.par	The value of the population parameters
FUN	The statistic as a function of random data
side	The type of the confidence interval (both sided, only lower bound or only upper bound)
conf.coeff	The confidence coefficient of the sampling interval
range	It controls the length of the interval in which the boundary points are searched for. One may increase the range in case the distribution of statistic is suspected to be fat tailed.
n	sample size
sim.size	simulation size, increasing it will gives more accuracy.

Details

The function asks the user to specify a distribution from which random sample is drawn and to specify a function of the random variables for which an approximate sampling Interval is to be provided. The function then uses Monte Carlo simulation technique to provide an approximate sampling interval of the statistic. This function might be useful when the sampling distribution for a particular statistic is unknown, but that statistic might be useful in drawing meaningful inference. Although this function is inferior to other sophisticated techniques to deal with this problem, it might come handy for a beginner.

Value

A list of class "momint" will be returned having the following components:

Method

The Method's Name

Population.Distrbution

The family of population distribution

Paramater

The parameter values of the population distribution

Statistic

The function of which the interval will be provided

Sample.Size

The sample size

Confidence.Coefficient

The confidence coefficient of the sampling interval

Sampling.Interval

The estimated sampling interval

Examples

sim_sam_int(dist="normal",pop.par=c(0,1),FUN=mean,side="both")
sim_sam_int(dist="binomial",pop.par=c(5,0.5),FUN=sum,side="lower")

MOM documentation built on Aug. 21, 2025, 5:54 p.m.