# Questions tagged [inverse-cdf]

Inverse cumulative distribution function, known also as quantile function, for a given probability returns the value at which the probability of observing some outcome from the random variable is less than or equal to the given probability.

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### inverse transform method [closed]

Using Inverse Transform Method to solve parts of the problem below: (a) Suppose $X \sim \text{Exponential}(λ = 0.2)$. Use RN to generate 20 random realisations of $X$ $\{X_1, X_2, .., X_{20}\}$ ...
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### How to simulate from a step (simple function) hazard function?

I have a step hazard function $h(t)$ (a simple function that jumps at specific times and it is constant between those jumps). Something like: How can I simulate survival times from this hazard ...
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### How to invert a mixture of log-logistic distributions? [duplicate]

Say I have a CDF of the form $$F(x) = \sum_{i=1}^n \frac{ k_i }{ 1 + (x/\alpha_i)^{ - \beta_i } }$$ $$\sum_{i=1}^n k_i = 1$$ How do I find the quantile function, i.e. how do I invert F for n>1? I ...
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### Prediction interval for OLS with non-normally distributed residuals

I'm estimating a multiple linear regression model (found in equation 19 of "The volatility of realized volatility", Corsi et al. https://www.econstor.eu/bitstream/10419/25467/1/515328057.PDF) using ...
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### Random Samples from Spliced Distribution

I am studying Clauset, Shalizi, and Newman, Power Law Distributions in Empirical Data (preprint available here) in R. Packages used: ...
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### Inverse-normal CDF approximation in Excel, Python or R

I read that the implementations of Inverse-normal cumulative distribution function (CDF) /quantile / ppf in R, Python (scipy) and Excel give similar results. However, I can't find the very formulae ...
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### CDF for inverse normal distribution [duplicate]

Do you have any idea how I can get the cumulative distribution function (CDF) for inverse-normal (Gauusian) distribution? Modeler 18.2 doesn't have that specific function, and I need it to calculate a ...
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### Confidence distribution for $\mu$ [closed]

Suppose that we have sample $x_{i}\sim N(\mu,\sigma^{2})\quad i=1,...,n$ and when $\sigma^{2}$ is known. A confidence distribution (CD) for $\mu$ can be written as follows (see, https://en.wikipedia....
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### Is there any relationship between random numbers sampled from some continuous distribution D and the quantile function of D?

I've noticed that when I sample n numbers from a continuous distribution D, sort them, and plot against the quantile function of D, both curves seem very similar. I've tried this for a few ...
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### How to calculate the inverse cdf for a sample with unknown distribution?

I'm stuck with an exercise that I'll just write down first: Based on a sample $x_1,...,x_{47}$, that can be considered coming from an unknown distribution, we study a qq-plot where the empirical ...
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### Using quantiles to estimate the parameters of a distribution: adjusting for unobserved extreme values

I with to estimate the parameters of a specified semi-infinite distributional family based on a sample drawn from that distribution. It is plausible that my sample median converges to the population ...
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### How to generate data that have given conditional mean and conditional quantile using R?

Suppose I want to generate independent data $(y_{i},x_{i})$ such that the conditional mean of $y_{i}$ given $x_{i}$ is a quadratic function in $x_{i}$ and the $.25$ conditional quantile of $y_{i}$ ...
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### Formula for Inverse T-distribution

I am trying to formulate an expression to calculate the critical value of a T-distribution for a given degrees of freedom. I have done so already for the Normal Distribution by considering the TI-84 ...
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### Why do I get 'Inf' value while doing quantile mapping in MATLAB?

I am doing bias correction of rainfall data simulated by Global Climate Model. Since, rainfall data generally follows gamma distribution, I am estimating parameter ...
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### Generate random numbers from a power-law/exponential distribution

I'm working through the paper Power-law distributions in empirical data by Clauset, Newman and Shalizi. On page 12, they generate random numbers from the following distribution: \begin{equation*} p(...
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### How to simplify the derivation of the inverse cdf yielded from l'Hospital rule?

I am currently dealing with a proof of Pauline Barrieu`s Paper "Assessing Financial Model Risk" (page 19). At one point she applys the l'Hospital rule on a limit equation. We have some cumulative ...
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### Nonparametric Quantile Regression for AR(1)-ARCH(1) process

I would like to estimate the conditional scale function $(\sigma_\tau(X_t))$ in a QAR-QARCH model represented by: Y_t = \mu_\tau(X_t) + \sigma_\tau(X_t)\epsilon_t,\, t = 1,2,\ldots \...
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### Monte Carlo Estimator for a quantile

I am trying to understand how to compute a crude Monte Carlo estimator for an $\alpha-$quantile. I have read the algorithm from the book Monte Carlo Methods and Models in Finance and Insurance, (Korn,...
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### Generate two distributions of data with consistent differences in quantile values

How can one generate two sets of data which are different at each quantile values (say decile)? Ex: 10th & 80th percentile is 4 & 22 respectively for the first set and the same should be 8 &...
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### What is the formula to calculate the nth percentile of Johnson-S$_U$ distribution with known parameters

I was wondering if there is a closed form to calculate the nth percentile of Johnson-S$_U$ distribution with known parameters? I know R could do this easily, but I want a formula instead so I can use ...
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### How should I inverse of the Normal loss function L(z) to be able to implement this in software?

I have a question related to this question: How to inverse loss function L(z) to normal standard distribution (z) The question wasn't answered since it wasn't clear what was asked. However I know ...
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### Inverse Transformation Sampling with Gaussian

For inverse transform sampling, if you know the CDF of a probability distribution ($f_X$) that you want to sample, you can generate a uniform realization ($U$) from [0,1], and then according to the ...
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### Input to fit a power-law to degree distribution of a network

I would like to use R to test whether the degree distribution of a network behave like a power-law with scale-free property. Nonetheless, I've read diferent people ...
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### Copula Behaviour : Gaussian vs Student T -Numerical Stability

I would like to get your opinion on the following topic: I am comparing the behaviour of Gaussian and Student-t Copulas. I employ the follwing procedure: Simulate N=100,000 samples from a Student ...
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### Generating a sample using inverse CDF method in python [closed]

How can I generate 1000-element sample using inverse CDF method? It should be easy but I'm a complete beginner. I know what it is mathematically but I don't know how to implement it in Python
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### How to convert a Johnson normalized variable back to a marginal variable

Edit after @eric_kernfeld answer. I'd like to do Generate a time-series, for example, from a uniform distribution. Transform of non-normal variable to standard normal distribution. Fit an arima ...
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### What is inverse CDF Normal Distribution Formula

Does anyone know what the Inverse Cumulative Distribution Function of Normal Distribution is? Does it have a closed form expression? I did not find any good answer using Google.