The **probability integral transform** transforms a random variable by its own CDF. It transforms a variable with a continuous distribution to a uniform distribution.
Questions tagged [pit]
8 questions
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What is the correlation between a random variable and its probability integral transform?
Are there known bounds on the $\operatorname{cor}(X,F(X))$? $X$ is a random variable with CDF $F(X)$. Let $X$ have a fixed variance, for example $\operatorname{var}(X)=1$. What $X$ can maximize or minimize the covariance?
sayda
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Assess calibration of a density forecast by Kolmogorov-Smirnov test on PIT of realized values
According to Elliott & Timmermann "Economic Forecasting" (2016) p. 429-430,
Calibration requires that if a density forecast assigns a certain probability to an event,
then the event should occur with the stated probability over successive…
Richard Hardy
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How to transfer the residuals to the uniform margin for copula-GARCH model in R?
I am studying the copula model in finance. To the best of my knowledge, I need to fit the GARCH model to my data (to each time series). Then, I need to get the residuals for each. After that, I need to transfer the residuals to uniform margins to…
Maryam
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Probability Integral Transforms (Not getting U(0,1))
I am trying to transform my GARCH standardized residuals to PITs in order to use them in a copula. The following code has been so far applied:
gjr_garch = arch_model(log_r['DAX'].dropna(), mean='AR', lags=8, vol='garch', p=1, o=1, q=1,…
deblue
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Evaluating Probabilistic/Bayesian Forecasts - PIT Values & How to Generate
Suppose you are modelling a linear regression $y_i = \alpha + \beta x_i + \epsilon_i$, in probabilistic terms:
$$ \mu_i = \alpha + \beta x_i, $$
$$ y_i \sim \mathcal{N}(\mu_i, \sigma). $$
For each new data point $x_{new}$, when making predictions,…
Mike Tauber
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Correlation between PITs of marginals of a bivariate normal distribution
Let a bivariate random vector $(X_1,X_2)\sim N(\mathbf{\mu},\Sigma)$ with correlation $\rho$. Let us apply probability integral transform (PIT) on each of the marginals to make them uniformly distributed and call the resulting random vector $(U_1,…
Richard Hardy
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Why do we say a probability integral transformed variable is uniform on the interval [0, 1]?
I am reading and trying to learn about the probability integral transform and some of its uses. From the CV question PIT on a sample with m bins, and KS test used to estimate a good value for m, the probability integral transform of random variable…
Alexis
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Understanding the methodology of evaluating density forecats
I have difficulties with under understanding the idea that Diebold came up with in 1998 in his essay about the evaluation of the accuracy of forecasting density p(y), he used the probability integral transform first to define that a variable Z:
and…
Jade li
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