How can we create right/left skewed normal distribution curve in R ?

[AbhishekHP]

How can we create skewed normal distribution curve in R ?
How to vary the skewedness using a variable ?
i.e. height of the peak and tail of the plot ?

Although many links say that they have an answer but non worked

Ploting a skewed normal distribution in R

generating skewed normal distribution in R

https://stackoverflow.com/questions/37055301/generating-skewed-distribution-in-r

This is in addition to earlier question:
How to calculate the cumulative area of the overlapped normal distribution curve in R ? - #2 by Yarnabrina solved by @Yarnabrina

# Tried 
library(fGarch)
library(tidyverse)
N <- 10000
x <- rnbinom(N, 10, .5)
dsnorm(x, mean = 0, sd = 1, xi = 1.5, log = FALSE)
# psnorm(x, mean = 0, sd = 1, xi = 1.5) %>% plot()
# qsnorm(x, mean = 0, sd = 1, xi = 1.5) %>% plot()
# rsnorm(x, mean = 0, sd = 1, xi = 1.5) %>% plot()

plot(dsnorm(x, mean = 0, sd = 1, xi = 1.5, log = FALSE))

[FJCC]

Your links suggest that you have used the sn package (https://cran.r-project.org/web/packages/sn/index.html) though the code you post does not mention it. In what way did sn not work?
Quoting from the sn package documentation -
*"dsn: Skew-Normal Distribution *
Description: Density function, distribution function, quantiles and random number generation for the skew-normal (SN) and the extended skew-normal (ESN) distribution."

[Yarnabrina]

@AbhishekHP

plot(dsnorm(x, mean = 0, sd = 1, xi = 1.5, log = FALSE))

I'm not sure I understand your problem. What exactly did you expect your result will be with this code? Note that x is not sorted, and you're plotting the points against 1:10000.

Here's an way to plot with ggplot2. I simulated in the range [-5, 5], but you can change as you prefer.

Note that the implementations in the packages fGarch and sn vary.

library(fGarch)
#> Loading required package: timeDate
#> Loading required package: timeSeries
#> Loading required package: fBasics
library(ggplot2)
library(sn)
#> Loading required package: stats4
#> 
#> Attaching package: 'sn'
#> The following object is masked from 'package:fBasics':
#> 
#>     vech
#> The following object is masked from 'package:stats':
#> 
#>     sd

central_tendency_sim <- 0
dispersion_sim <- 1
skewness_sim <- 1.5

N_sim <- 10000

obs_sim <- seq(from = -5,
               to = 5,
               length.out = N_sim)

ggplot(data = data.frame(u = obs_sim),
       mapping = aes(x = u)) +
  stat_function(mapping = aes(colour = "fGarch"),
                fun = dsnorm,
                args = list(mean = central_tendency_sim,
                            sd = dispersion_sim,
                            xi = skewness_sim)) +
  stat_function(mapping = aes(colour = "sn"),
                fun = dsn,
                args = list(xi = central_tendency_sim,
                            omega = dispersion_sim,
                            alpha = skewness_sim)) +
  stat_function(mapping = aes(colour = "standard"),
                fun = dnorm) +
  scale_colour_manual(name = NULL,
                      values = c("red", "blue", "green"))

^{Created on 2019-09-06 by the reprex package (v0.3.0)}

In case you want to plot in base R, that also works.

library(fGarch)
#> Loading required package: timeDate
#> Loading required package: timeSeries
#> Loading required package: fBasics
library(sn)
#> Loading required package: stats4
#> 
#> Attaching package: 'sn'
#> The following object is masked from 'package:fBasics':
#> 
#>     vech
#> The following object is masked from 'package:stats':
#> 
#>     sd

central_tendency_sim <- 0
dispersion_sim <- 1
skewness_sim <- 1.5

N_sim <- 10000

obs_sim <- seq(from = -5,
               to = 5,
               length.out = N_sim)

den_sim_fGarch <- dsnorm(x = obs_sim,
                         mean = central_tendency_sim,
                         sd = dispersion_sim,
                         xi = skewness_sim)

den_sim_sn <- dsn(x = obs_sim,
                  xi = central_tendency_sim,
                  omega = dispersion_sim,
                  alpha = skewness_sim)

par(mfrow = c(2, 2))

plot(x = obs_sim,
     y = den_sim_fGarch,
     type = "l",
     xlab = "observations",
     ylab = "densities",
     main = "plot points and join - fGarch",
     col = "violetred")
curve(expr = dnorm,
      from = -5,
      to = 5,
      n = N_sim,
      add = TRUE,
      col = "limegreen",
      lty = 2)

plot(x = obs_sim,
     y = den_sim_sn,
     type = "l",
     xlab = "observations",
     ylab = "densities",
     main = "plot points and join - sn",
     col = "navyblue")
curve(expr = dnorm,
      from = -5,
      to = 5,
      n = N_sim,
      add = TRUE,
      col = "limegreen",
      lty = 2)

plot.function(x = function(t) dsnorm(x = t,
                                     mean = central_tendency_sim,
                                     sd = dispersion_sim,
                                     xi = skewness_sim),
              to = 5,
              from = -5,
              n = N_sim,
              xlab = "observations",
              ylab = "densities",
              main = "plot function - fGarch",
              col = "palevioletred")
curve(expr = dnorm,
      from = -5,
      to = 5,
      n = N_sim,
      add = TRUE,
      col = "limegreen",
      lty = 2)

plot.function(x = function(t) dsn(x = t,
                                  xi = central_tendency_sim,
                                  omega = dispersion_sim,
                                  alpha = skewness_sim),
              to = 5,
              from = -5,
              n = N_sim,
              xlab = "observations",
              ylab = "densities",
              main = "plot function - sn",
              col = "skyblue")
curve(expr = dnorm,
      from = -5,
      to = 5,
      n = N_sim,
      add = TRUE,
      col = "limegreen",
      lty = 2)

dev.off()
#> null device 
#>           1

^{Created on 2019-09-06 by the reprex package (v0.3.0)}

[AbhishekHP]

Thanks @Yarnabrina a ton for helping me here.

Actually, I made a sketch to describe clearly and attached.
Black curve has peak at x = .2 but ranges from 0 - 1
Therefore, it got to be skewed to one side.

[AbhishekHP]

Actually, in those link, it is hardly understandable because there were no plots and just random script
Hard to even understand the solution.

[AbhishekHP]

@Yarnabrina

Do you mean to draw two densities (red and black)?

No, Just a black one is enough.

[FJCC]

If you want to generate a distribution that peaks near 0.2 and has most of its density between 0 and 1, the following call to dsn() from the sn package comes close.

library(sn)
 
X <- seq(-1, 2, 0.01)
plot(X, dsn(X, xi = 0.1, omega = 0.3, alpha = 5), type = "l")
abline(v = 0.2)

^{Created on 2019-09-06 by the reprex package (v0.2.1)}