Description Usage Arguments Details Value Functions Author(s) References See Also Examples
Density distribution function, quantile function and random generation function for the split normal distribution.
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x |
vector of quantiles. |
mu |
vector of location parameter. (The mode of the density) |
sigma |
vector of standard deviations. |
lmd |
vector of skewness parameters (>0). If is 1, reduced to symmetric normal distribution. |
logarithm |
logical; if TRUE, probabilities p are given as log(p). |
q |
vector of quantiles. |
p |
vector of probability. |
n |
number of observations. If length(n) > 1, the length is taken to be the number required. |
The random ' variable y follows a split-normal distribution, y~N(μ, ' σ, λ), which has density:
1/(1+λ)σ ' √(2/π) exp{-(y-μ)*2/2σ^2}, if y<=μ
'
1/(1+λ)σ √(2/π) exp{-(y-μ)*2/2σ^2 λ^2}, ' if y>μ
where σ>0 and λ>0. The Split-normal ' distribution reduce to normal distribution when λ=1.
dsplitn
gives the density; psplitn
gives the percentile;
qsplitn
gives the quantile; and rsplitn
gives the random
variables. Invalid arguments will result in return value NaN, with a warning.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
psplitn
: Percentile for the split-normal distribution.
qsplitn
: Quantile for the split-normal distribution.
rsplitn
: Randon variables from the split-normal distribution.
Feng Li, Jiayue Zeng
Villani, M., & Larsson, R. (2006) The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis. Sveriges Riksbank Working Paper Series, No. 175.
splitn_mean()
,
splitn_var()
,splitn_skewness()
and
splitn_kurtosis()
for numerical characteristics of the
split-normal distribution.
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