对数正态分布(替代参数化)

Question

我想知道EvaStats包(基于AM，GM，log10)中的替代参数化是如何做到的；我尝试了log10，但失败了！帮助

x=c(1151, 453, 1530, 2852, 1382)
meanx=mean(x);sdx=sd(x); cvx=sd/mean; 
meanx; sdx; cvx

1 1473.6；1 874.2501；1 0.5932751

y1=log(x)   # log(e) base
mean1=mean(y1);sd1=sd(y1); cv1=sd1/mean1;
mean1; sd1; cv1; 

1 7.136873；1 0.6648726；1 0.09316022

现在是对数正态分布(另一种参数化)；

library(EnvStats)
(p=seq(0.1,1,0.1)); 
qlnormAlt(p, mean =meanx, cv=cvx) 

PX≤x==> 1 626.9803 798.3150 950.2311 1102.7414 1267.3461 1456.5211 # 1690.2899 8 2011.9454 2561.7490 Inf

qlnorm(p, meanlog = mean1, sdlog = sd1, lower.tail =TRUE,  log.p = FALSE)

PX≤x==> 1 536.3594 718.5980 887.3269 1062.5527 1257.4901 1488.1910 1782.0729 #8 2200.5088 2948.1747 Inf ( excel中的结果相同)

Answer 1

案例:转换为基本R对数正态到EnvStats对数正态

# For base R  log-normal parameters
meanlog <- 0
sdlog <- 1

# convert to log-normal alt parameters
alt_cv <- sqrt(exp(sdlog^2) - 1)
alt_mean <- exp(meanlog + (sdlog^2)/2)

#Generate random variate
x <- rlnorm(10, meanlog = meanlog, sdlog = sdlog)

#The densities from ALT parameterization EnvStats
dlnormAlt(x, mean = alt_mean, cv = alt_cv, log = FALSE)
#0.07143345 0.02845393 0.65249008 0.55945034 0.12051190 0.51631108 
#0.60456145 0.61928177 0.18041191 0.64513395

# From dlnorm
dlnorm(x, meanlog = meanlog, sdlog = sdlog, log = FALSE)
#0.07143345 0.02845393 0.65249008 0.55945034 0.12051190 0.51631108 
#0.60456145 0.61928177 0.18041191 0.64513395

案例:将EnvStats对数正态转换为基本R对数正态

library(EnvStats)

# in log-normal alt
alt_mean <- 1.648721      # = exp(1/2)
alt_cv <- 1.310832        # = sqrt(exp(1) - 1)

# convert to base R log-normal
sdlog <- sqrt(log(1 + alt_cv^2))
meanlog <- log(alt_mean) - (sdlog^2)/2

# Check if this is correct by generating a sample and 
# estimating density

#Generate random variate
x <- rlnormAlt(10, mean = alt_mean, cv = alt_cv)

#The densities from ALT parameterization EnvStats
dlnormAlt(x, mean = alt_mean, cv = alt_cv, log = FALSE)
#0.40210537 0.12318313 0.65370439 0.21540401 0.59956874 0.63914847 
#0.05152114 0.04156760 0.48919495 0.05110028

# From dlnorm
dlnorm(x, meanlog = meanlog, sdlog = sdlog, log = FALSE)
#0.40210537 0.12318313 0.65370439 0.21540401 0.59956874 0.63914847 
#0.05152114 0.04156760 0.48919495 0.05110028