Can we write skew normal distribution (2) in terms of theta, x ,y
35 次查看(过去 30 天)
显示 更早的评论
I was trying to write skew normal distribution in terms of theta, x , y , rather than using covariance matrix
is there any equation like it is for bivariate equation
Thanks in advance
0 个评论
回答(1 个)
Aditya
2023-9-14
编辑:Aditya
2023-9-14
Hey Prakash,
I understand that you require a different way of writing skew normal distribution in terms of different variables.
Yes, the skew normal distribution can be defined in terms of parameters theta, x, and y instead of using a covariance matrix. The skew normal distribution is a generalization of the normal distribution that includes an additional parameter for skewness.
function pdfValue = skewNormalPDF(x, theta, alpha, omega)
% Skew Normal PDF implementation
% x: random variable
% theta: location parameter
% alpha: shape parameter controlling skewness
% omega: scale parameter
% Standard normal PDF and CDF
phi = @(x) exp(-0.5 * x.^2) / sqrt(2 * pi);
Phi = @(x) 0.5 * (1 + erf(x / sqrt(2)));
% Calculate the skew normal PDF
z = (x - theta) / omega; % Standardize the random variable
pdfValue = 2 / omega * phi(z) .* Phi(alpha * z);
end
It's important to note that the skew normal distribution is a univariate distribution, meaning it models a single random variable. If you want to extend it to a multivariate distribution, you would need to use a multivariate skew normal distribution or another appropriate multivariate distribution that accommodates skewness, such as the skew-t distribution.
You may refer to the following link for further information:
Thanks,
Best Regards
Aditya Kaloji
0 个评论
另请参阅
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!