Linked Questions
16 questions linked to/from Help me understand the quantile (inverse CDF) function
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How does the inverse transform method work?
How does the inversion method work?
Say I have a random sample $X_1,X_2,...,X_n$ with density $f(x;\theta)={1\over \theta} x^{(1-\theta)\over \theta}$ over
$0<x<1$ and therefore with cdf $F_X(x)=...
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Inverse function for a non-decreasing CDF
For a CDF that is not strictly increasing, i.e. its inverse is not defined, define the quantile function
$$F^{-1} (u) =\inf \{x: F(x) \geq u \},\quad 0<u<1. $$
Where U has a uniform $(0,1)$ ...
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Using Standard Deviation and Flipping Coins
I want to create a simple project to show about ESP.
I started with the idea of guessing whether a coin would be heads or tails.
I first wanted to show some values by pure guessing.
So, using ...
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7
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Questions regarding proof of probability integral transform
I'm attempting to understand the proof of the probability integral transform in [1].
First they define $Y = F_X ( X )$. Yet, the cumulative distribution function is defined in [2] as
$$F_X ( x ) = P(...
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4
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3
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How to convert percentage values from 7 point scale to 5 point scale?
Suppose in one year I had a survey with 7-point scale and the values are like
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2
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Calculating probability that a probability of heads lies in a given interval
Suppose you flip a coin $n$ times and you get heads $x$ times where $x < n$.
By what confidence can you say that the probability of the coin showing heads during a random toss lies between $U_1$ ...
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2
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1
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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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4
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Intuition behind F(X) following a uniform distribution
Consider the following theoreom: If a random variable $X$ has CDF $F,$ then $F(X)\sim U[0,1]$ where $F(.)$ is the c.d.f of $X$.
The demonstration is very straightforward:
$\mathbb{P}\left(F\left(X\...
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2
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2
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the two step approach
I have a continuous variable which is not normally distributed i want to transform it to normal using the two step approach method in the link below:
Abstract This article describes and demonstrates ...
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Two tailed test on beta distribution
I have a serie of data ranging between [0,1]. I'm trying to fit this data using beta distributions. Given an extra point, between the same range, I would like to obtain a significance respect to the ...
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8
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1
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Sample uniformly from unit square conditioned on sum and product
Consider the following conditional distributions:
\begin{align}
X, Y \stackrel{\text{iid}}{\sim} U(0, 1) &\mid X + Y = a & a \in [0, 2] \\
X, Y \stackrel{\text{iid}}{\sim} U(0, 1) &\mid X ...
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How can I get confidence interval from Laplace distribution in python?
I have a dataset and I checked that fits a Laplace distribution. I want to get different confidence intervals from it.
I know that in a normal distribution, the confidence interval of 68% is mean + ...
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0
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2
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How to correctly bucket data into quantiles: by index or by value?
I've been recently involved in a discussion surrounding the assignment of individual values to n-tiles.
One way of doing it would be to rank all of the data in ascending order, dividing it into $n$ ...
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0
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1
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Beta Binomial Inverse CDF
There are p groups of size $n_1, n_2, ... , n_p$ each with number of successes $x_1, x_2, ... x_p$ and number of failures $n_1 - x_1, n_2 - x_2, ... , n_p - x_p$.
$X_i$ ~ $Binom( n_i, p_i)$, where $...
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1
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1
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Am I doing this right with a Gaussian Distribution?
I have the following code in MATLAB, which I believe calculates the probability of a certain point (p) in the normal distribution. I know sigma (variance) and mu (mean) based on calculations.
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