bpAcc (version 0.0-2)

psigmaami: Distribution function of the sigma-aami transformation (not vectorized).

Description

Distribution function of the sigma-aami transformation (not vectorized).

Usage

psigmaami(sigmaami, mu, std.dev, n, ptolerror = 0.85, lower.tail = TRUE)

Value

psigmaami gives the distribution function.

Arguments

sigmaami

A single, positive, quantile. See below for further details.

mu, std.dev

mean and standar deviation of the average errors distribution (normal).

n

sample size

ptolerror

Probability of tolerable error, Default is 0.85

lower.tail

logical; it TRUE (default), probabilities are \(P[sigmaami \le x]\) otherwise, \(P[sigmaami > x]\).

Author

Tanvi Chandel, Tet-Chuan Lee, Andrew Lowe, Victor Miranda.

Details

This is the distribution function of the sigmaami transformation.

A size-n sample of blood pressure average errors (average of the difference between three device measurements and the three corresponding reference readings) is drawn from a normal distribution with mean mu and standard deviation std.dev. The r.v. sigmaami results from transforming \(xbar\), the sample mean, assuming the proportion of drawn errors lie in (-delta, delta) with probability ptolerror, that is sigmaami\(=sigmaami(xbar)\).

References

Chandel, T. and Lee, TC. and Lowe, A. and Miranda, V. (2022) Blood Pressure Device Accuracy Evaluation: Statistical Considerations with an Implementarion in R, Statistical Methods in Medical Research (under review).

See Also

ProbAccept

Examples

## Sample of n = 85 average errors from a normal distribution with mean 3 and st.dev = 2.
psigmaami(sigmaami = 4, mu = 3, std.dev = 2, n = 85)