est.density.q1q2q3 | R Documentation |
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).
est.density.q1q2q3(
q1 = NULL,
med = NULL,
q3 = NULL,
n = NULL,
opt = TRUE
)
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 |
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.
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.
Alysha De Livera, Luke Prendergast, and Udara Kumaranathunga. A novel density-based approach for estimating unknown means, distribution visualisations, and meta-analyses of quantiles, 2024. Pre-print available here: https://arxiv.org/abs/2411.10971.
Warren Gilchrist. Statistical modelling with quantile functions. Chapman and Hall/CRC, 2000.
P. J. van Staden and R. A. R. King. The quantile-based skew logistic distribution. Statistics & Probability Letters, 96:109–116, 2015.
R. King and P. van Staden. sld: Estimation and Use of the Quantile-Based Skew Logistic Distribution. R package version 1.0.1, 2022. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32614/CRAN.package.sld")}. https://CRAN.R-project.org/package=sld.
est.density.five()
, est.density.minq2max()
#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.density.q1q2q3(q1 = quants[1], med = quants[2], q3 = quants[3],
n=n, opt=TRUE)$parameters
params
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