skew: Skewness function
In jiperezga/DistMom: Distribution moments or distribution cumulants.

Description Usage Arguments Details Value Note Author(s) See Also Examples

Calcule theoretical skewness of any continuous or discrete distribution.

1	skew(dist, param, domain)

`dist`	density or mass name for the distribution. The created density or mass functions must have a name of the form `dxxx`. To understand its use see details and examples.
`param`	are the parameters of the distribution. The name of each parameter must be specified. To understand its use see examples.
`domain`	defines the domain of the distribution function. The type of domain of distribution to be tried see details.

The skew function supports probability distribution functions of a large number of libraries.

In the dist argument, you must enter the name of the distribution of interest, for example, you can enter "gamma" or "dgamma", both will produce the same result.

If f(x) has no parameters, then do param = NULL.

The following are the different domain argument:

binom: for discrete distributions of binomial type.
counts: for discrete distributions of counting type.
realline: for continuous distributions defined between -∞ and ∞.
realplus: for continuous distributions defined between 0 and ∞.
real0to1: for continuous distributions defined between 0 and 1.
real-1to1: for continuous distributions defined between -1 and 1.
c(lower = a, upper = b): for continuous distributions defined between a and b.

skew gives the theorical skewness of any continuous or discrete probability distribution function.

Many continuous distributions support domain = "realline" even though they are not defined from -∞ to ∞ because of their programming.

In the same way, many discrete distributions support domain = "counts" even though they are not defined from 0 to ∞ or 1 to ∞ because of their programming.

It is recommended to try initially with this argument.

Discrete distributions require the existence of the quantile function, of the form qxxx.

Jorge Iván Pérez, jivan.perez@udea.edu.co

Distributions for other standard distributions.

moments, cumulants, kurt.

# Let's try first with distributions of the library stats
skew(dist = "dchisq", param = c(df = 3), domain = "realplus")
# or
skew(dist = "chisq", param = c(df = 4), domain = "realplus")

#---------------------------------------------------------------------------------------

# The name of the created density functions must have a name
# of the form dxxx. Also, how does it not have parameters
# then param = NULL
dmyfunction <- function(x) x^3/4 
# so that it integrates to 1, x must be between 0 to 2.
skew(dist = "dmyfunction", param = NULL, domain = c(0, 2))

#---------------------------------------------------------------------------------------

# Let's try distributions from other libraries
if(!require("extraDistr")) install.packages("extraDistr") # to install the package
# The same result is obtained with the diferent domain (see 'Note')

skew(dist = "dpareto", param = c(a = 4, b = 10),
     domain = "realline")
        
# In this case, no moments are calculated for k> 3, because the
# parameter of the pareto distribution is a = 4, and
# therefore, the moments are defined for E(X^k) < a.
# Read about pareto distribution for more information.       

skew(dist = "dbhatt", param = c(mu = 3, sigma = 7),
     domain = "realline")
 
#---------------------------------------------------------------------------------------

# Let's try distributions from other libraries
if(!require("gamlss.dist")) install.packages("gamlss.dist") # to install the package
skew(dist = "PE", param = c(mu = -25, sigma = 7, nu = 4),
     domain = "realline") 
skew(dist = "BEOI", param = c(mu = 0.3, sigma = 7, nu = 0.3),
     domain = "real0to1") 
skew(dist = "BCT", param = c(mu = 12, sigma = 0.2, nu = 3,
     tau = 5), domain = "realplus")
skew(dist = "SEP2", param = c(mu = 0.5, sigma = 3,
     nu = 0, tau = 5), domain = "realline")

#---------------------------------------------------------------------------------------

# Let's try with a discrete counting distribution
if(!require("gamlss.dist")) install.packages("gamlss.dist") # to install the package
skew(dist = "DEL", param = c(mu = 2, sigma = 3, nu = 0.5),
     domain = "counts")
skew(dist = "NBF", param = c(mu = 4, sigma = 3, nu = 2),
     domain = "counts")
        
#---------------------------------------------------------------------------------------

# Let's try with a discrete binomial type distribution
skew(dist = "binom", param = c(size = 15, prob = 0.3),
        domain = "binom")
skew(dist = "dhyper", param = c(m = 10, n = 7, k = 8),
        domain = "binom")