Probability finding the characteristics
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Hello What should I add to this code to Evaluate the characteristic function of 𝛷𝑌(𝜔) and plot |𝛷𝑌(𝜔)|.
% initialising given data :
a = 38 ; b = 150 ; mean_x = 90 ; var_x = 40 ;
% defining sample space :
N = 1000 ; x = linspace (a,b,N) ;
% defining the normal distribution :
f = @(x) (1/(var_x * sqrt(2*pi))) * exp(-0.5*((x - mean_x)/var_x).^2) ;
% defining the cumulative normal distribution :
F = @(x) integral(f,-inf,x) ;
% defining the truncated normal distribution :
ft = @(x) f(x)/(F(b)-F(a)) ;
% calculating the data points :
f_data = f(x) ; % normal distribution ft_data = ft(x) ; % truncated distribution
% plotting the data points : plot(f_data , x); % plotting normal distribution (the blue one) hold on plot(ft_data , x); % plotting truncated distribution (the red one) hold off
% finding the equation for first moment of the truncated distribution : m_1 = @(x) (ft(x)).*(x) ; M_1 = integral (m_1,a,b)
% finding the equation for second moment of the truncated distribution : m_2 = @(x) (ft(x)).*(x.^2) ; M_2 = integral (m_2,a,b)
% finding the equation for third moment of the truncated distribution : m_3 = @(x) (ft(x)).*(x.^3) ; M_3 = integral (m_3,a,b)
% finding the equation for forth moment of the truncated distribution : m_4 = @(x) (ft(x)).*(x.^4) ; M_4 = integral (m_4,a,b)
% finding the equation for fifth moment of the truncated distribution : m_5 = @(x) (ft(x)).*(x.^5) ; M_5 = integral (m_5,a,b)
% finding the variance of the truncated distribution with the help of first and second moments : var_t = M_2 - (M_1).^2
% defining new limits : A = a.^2 ; B = b.^2 ;
% defining new sample space : y = x.*(x);
% plotting the new PDF : plot(f(y),y);
% finding the first moment : my_1 = @(y) (f(y)).*(y) ; My_1 = integral (my_1,A,B)
% finding the first moment : my_2 = @(y) (f(y)).*(y.^2) ; My_2 = integral (my_2,A,B)
% finding the first moment : my_3 = @(y) (f(y)).*(y.^3) ; My_3 = integral (my_3,A,B)
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