semiconttol.int {tolerance}

Generalized Intervals for Semicontinuous Data

Description

Provides confidence intervals, one-sided prediction limits, and one-sided tolerance limits for semicontinuous data — either zero-inflated gamma (ZIG) or zero-inflated lognormal (ZILN) distribution — using a generalized fiducial framework.

Usage

semiconttol.int(x, alpha = 0.05, P = 0.99, N = 1000)

Arguments

x

A vector of semicontinuous data.

alpha

The level chosen such that 1-alpha is the confidence level.

P

The proportion of the population to be covered by this tolerance interval.

N

The number of fiducial samples to generate.

Value

semiconttol.int returns a list with items:

ZIG.CI

The generalized confidence interval under a ZIG distribution.

ZIG.PI

The generalized (upper) prediction limit under a ZIG distribution.

ZIG.TI

The generalized (upper) tolerance limit under a ZIG distribution.

ZIG.TI.appx

The generalized (upper) tolerance limit under a ZIG distribution based on the Wilson-Hilferty approximation.

ZILN.CI

The generalized confidence interval under a ZILN distribution.

ZILN.PI

The generalized (upper) prediction limit under a ZILN distribution.

ZILN.TI

The generalized (upper) tolerance limit under a ZILN distribution.

ZILN.TI.appx

The generalized (upper) tolerance limit under a ZILN distribution based on an approximation used in Hasan and Krishnamoorthy (2018).

`NA`

The number of times generalized fiducial quantities could not be calculated due to unlucky samples being drawn; e.g., a sample with all 0s. This will happen rarely and usually only when there is a very large proportion of zeros.

References

Hasan, M. S. and Krishnamoorthy, K. (2018), Confidence Intervals for the Mean and a Percentile Based on Zero-Inflated Lognormal Data, Journal of Statistical Computation and Simulation, 88, 1499–1514.

Zou, Y. and Young, D. S. (2024), Fiducial-Based Statistical Intervals for Zero-Inflated Gamma Data, Journal of Statistical Theory and Practice, 18, 1–20.

See Also

fidbintol.int, fidnegbintol.int, fidpoistol.int

Examples

 
## Generalized intervals assuming 95% confidence and
## 95% content for a dataset analyzed in Hasan and
## Krishnamoorthy (2018).

x <- c(6, 0, 6, 9, 6.5, 0, 0, 0, 1, 0.5, 2, 2, 0, 0, 1)
set.seed(1)
out <- semiconttol.int(x, P = 0.95, alpha = 0.05, N = 500)
out