Can we write skew normal distribution (2) in terms of theta, x ,y

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

Answer 1

[Aditya]

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:

https://www.mathworks.com/help/stats/normpdf.html

Thanks,

Best Regards

Aditya Kaloji