tobitinv

tobitinv computes the inverse of the tobit cumulative distribution function.

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Syntax

Description

example

x =tobitinv(p) Using all default options.

example

x =tobitinv(p, mu) mu is specified.

example

x =tobitinv(p, mu, sigma) mu sigma are specified.

example

x =tobitinv(p, mu, sigma, left) mu sigma and left are specified.

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x =tobitinv(p, mu, sigma, left, right) Check accuracy of results, monitoring $|x-F_{tobit}^{-1} (F_{tobit}(x))|$.

Examples

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  • Using all default options.

    • In this case we assume that mu=0, sigma=1, left=0, right=Inf 

    x=tobitinv(0.5)

  • mu is specified.

    • In this case we assume that sigma=1, left=0, right=Inf 

    x=tobitinv(0.8,1)

  • mu sigma are specified.

    • In this case we assume that left=0, right=Inf 

    x=tobitinv(0.8,1,0.4)

  • mu sigma and left are specified.

    • In this case we assume that right=Inf 

    x=tobitinv(0.95,2.5,0.4,3)

  • Check accuracy of results, monitoring $|x-F_{tobit}^{-1} (F_{tobit}(x))|$.

    • a=100; 
b=200;
mu=(a+b).*0.6;
sigma=40;
x=tobitrnd(mu,sigma,a,b,100,1);
Y=zeros(length(x),1);
Ychk=Y;
for i=1:length(x)
Y(i)=x(i)-tobitinv(tobitcdf(x(i),mu,sigma,a,b),mu,sigma,a,b);
end
disp('Maximum deviation from 0');
disp(max(max(abs(Y))));
    Maximum deviation from 0
     0

    Input Arguments

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    p — Probability at which the inverse of the cdf must be evaluated $0 \leq p \leq 1$. Scalar, vector or matrix 3D array of the same size of x and b.

    A scalar input functions as a constant matrix of the same size as the other input.

    See the section called "More About:" for more details about the inverse gamma distribution.

    Data Types: single | double

    Optional Arguments

    mu — location parameter of the tobit distribution. Scalar, vector or matrix 3D array of the same size of x and sigma, Lower, Upper.

    A scalar input functions as a constant matrix of the same size as the other input. Default value of mu is 0.

    See "More About:" for details about the tobit distribution.

    Example: 'mu',10

    Data Types: single | double

    sigma — scale parameter of the tobit distribution. Scalar, vector or matrix 3D array of the same size of x and sigma, Lower, Upper.

    A scalar input functions as a constant matrix of the same size as the other input. Default value of sigma is 1 See "More About:" for details about the tobit distribution.

    Example: 'sigma',800

    Data Types: single | double

    left — lower limit for the censored random variable. Scalar.

    If set to -Inf, the random variable is assumed to be not left-censored; default value of left is zero (classical tobit model).

    Example: 'left',1

    Data Types: double

    right — right limit for the censored random variable. Scalar.

    If set to Inf, the random variable is assumed to be not right-censored; default value of left is Inf (classical tobit model).

    Example: 'right',800

    Data Types: double

    Output Arguments

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    x —inverse CDF value. Scalar, vector or matrix or 3D array of the same size of input arguments p, mu, sigma, left, right

    $p=\int_0^x f_{tobit}(t | \mu, \sigma, left, right) dt$ is the inverse of tobit cdf with parameters mu, sigma, left, right for the corresponding probabilities in p.

    More About

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    Additional Details

    The cdf of the tobit distribution defined over the support $x \in R $ with location parameter $mu$, scale parameter $sigma$ and lower and upper censor values left and right \[ F_{tobit}(x, \mu, \sigma, left, right) =\int_0^x f(t) dt \]

    References

    Greene, W.H. (2008), "Econometric Analysis, Sixth Edition", Prentice Hall, pp. 871-875.

    Tobin, J. (1958), Estimation of Relationships for Limited Dependent Variables, "Econometrica", 26, pp. 24-36.

    See Also

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