metaquant (version 0.1.3)

est.sld.q1q2q3: Estimating Unknown Parameters using First Quartile, Median and Third Quartile

Description

This function provide estimates for the parameters of skew logistic distribution (SLD), the sample mean and the standard deviation using 3-number summary {first quartile (\(q_1\)), median (\(q_2\)), third quartile (\(q_3\))} from a study with sample size \(n\), using the method explained in De Livera et al. (2024).

Usage

est.sld.q1q2q3(
   q1 = NULL, 
   med = NULL, 
   q3 = NULL, 
   n = NULL, 
   opt = TRUE
   )

Value

A list with following components:

• parameters: named numeric vector representing the estimated parameters ('location', 'scale', 'skewing') of SLD.

• mean: numeric value of the estimated mean of the sample using SLD.

• sd: numeric value of the estimated standard deviation of the sample using SLD.

Arguments

q1

numeric value representing the first quartile of the sample.

med

numeric value representing the median of the sample.

q3

numeric value representing the third quartile of the sample.

n

numeric value specifying the sample size.

opt

logical value indicating whether to apply the optimisation step in estimating parameters using theoretical quantiles. The default value is TRUE.

Details

De Livera et al. (2024) proposed using the skew logistic distribution (SLD) to estimate unknown parameters for studies reporting 3-number summaries in the meta-analysis context.

The quantile-based skew logistic distribution, introduced by Gilchrist (2000) and further modified by van Staden and King (2015) is used to approximate the sample's distribution using 3-point summaries. The SLD quantile function is defined using three parameters: a location parameter (\(\lambda\)), a scale parameter (\(\eta\)), and a skewing parameter (\(\delta\)). The parameters of the SLD are estimated by formulating and solving a set of simultaneous equations which relate the estimated sample quantiles to their theoretical counterparts of the SLD.

References

De Livera, A. M., Prendergast, L., & Kumaranathunga, U. (2024). A novel density-based approach for estimating unknown means, distribution visualisations and meta-analyses of quantiles. arXiv preprint arXiv:2411.10971. https://arxiv.org/abs/2411.10971.

Gilchrist, W. (2000). Statistical modelling with quantile functions. Chapman & Hall/CRC.

van Staden, P. J., & King, R. A. R. (2015). The quantile-based skew logistic distribution. Statistics & Probability Letters, 96, 109–116.

King, R., & van Staden, P. (2022). sld: Estimation and use of the Quantile-Based Skew Logistic Distribution (R package Version 1.0.1). Comprehensive R Archive Network (CRAN). https://doi.org/10.32614/CRAN.package.sld. https://CRAN.R-project.org/package=sld.#'

See Also

est.gld.five(), est.sld.minq2max()

Examples

#Generate 3-number summary data
set.seed(123)
n <- 1000
x <- stats::rlnorm(n, 4, 0.3)
quants <- c(stats::quantile(x, probs = c(0.25, 0.5, 0.75)))

#Estimate SLD parameters using 3-number summary
params<- est.sld.q1q2q3(q1 = quants[1], med = quants[2], q3 = quants[3], 
                            n=n, opt=TRUE)$parameters
params