Questions tagged [cumulative-distribution-function]

Cumulative distribution function. While the PDF gives the probability density of each value of a random variable, the CDF (often denoted $F(x)$) gives the probability that the random variable will be less than or equal to a specified value.

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7
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4answers
8k views

What is the proper way to estimate the CDF for a distribution from samples taken from that distribution?

Given $n$ samples from a (continuous) distribution X, the obvious thing to do is sort them, and distribute them equally across $[0,1]$ by taking $(x_{(k)}, (k-1/2)/n)$ as estimates of particular ...
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2answers
288 views

Trouble using pareto levy stable distribution software [closed]

I'm using an arcane free program off the internet called "stable.exe" trying to fit a stable distribution curve to a dataset, but I'm having trouble entering the dataset file into the program. When ...
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1answer
8k views

Distribution of a ratio of uniforms: What is wrong?

Suppose that $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$ Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $. Now, I came up with two ways of doing this. ...
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3answers
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Expected value of a random variable in a range

I have a random variable $x$ with $E(x) = \mu$ and PDF $f(x)$ and CDF of $F(x)$. Is there any way to represent the $E(x|x<\bar{x})$ in terms of $\mu$ and $f(x)$ or $F(x)$? i.e. to write the ...
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2answers
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What is the best way to discretize a 1D continuous random variable?

Say I have a 1-dimensional continuous random variable $X$, with PDF $f(X)$, CDF $F(X)$ and inverse CDF $F^{-1}$. What is the best way to discretize $X$? To keep things clear, let $Y$ denote the ...
4
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1answer
4k views

Can a negative binomial distribution be used to model a continuous distribution?

I have a data set which is a set of continuous distances from some origin. I originally modeled this as a negative binomial distribution by rounding the data and using it as an input in the Matlab ...
3
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1answer
984 views

Calculating event probabilities in mixed, discrete/continuous distributions

This is a simple question. I am dealing with a "clipped" normal distribution -- say, $N(0,0.5)$ clipped between $[-1,1]$. I would like to calculate the "probability" of a sample, but I know that in $...
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3answers
1k views

CDF raised to a power?

If $F_Z$ is a CDF, it looks like $F_Z(z)^\alpha$ ($\alpha \gt 0$) is a CDF as well. Q: Is this a standard result? Q: Is there a good way to find a function $g$ with $X \equiv g(Z)$ s.t. $F_X(x) = ...
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0answers
414 views

How can I convert kernel quantiles into sample quantiles?

I calculated the quantiles for an Epanechnikov kernel which I'm using to estimate the density of a sample. What I need is to find the sample quantiles knowing that it is composed of many Epanechnikov ...
7
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1answer
979 views

What is the closed form solution for the inverse CDF for Epanechnikov

Is there a closed form solution for this inverse CDF?
7
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2answers
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Use Empirical CDF vs Distribution CDF?

NOTE: I purposely did not label the axis due to pending publications. The line colors represent the same data in all three plots. I fitted my data using a negative binomial distribution to generate a ...
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2answers
313 views

Efficient Empirical CDF Computation / Storage

I'm trying to precompute the distributions of several random variables. In particular, these random variables are the results of functions evaluated at locations in a genome, so there will be on the ...
5
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1answer
244 views

How can I control the false positives rate?

I feel I'm pretty new to this, since some time passed since my last statistics assignment, so please bear with me. I am analyzing results of a biological experiment. Basically, I'm looking at a some ...
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2answers
973 views

Computing the cumulative distribution of max drawdown of random walk with drift

I am interested in the distribution of the maximum drawdown of a random walk: Let $X_0 = 0, X_{i+1} = X_i + Y_{i+1}$ where $Y_i \sim \mathcal{N}(\mu,1)$. The maximum drawdown after $n$ periods is $\...
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3answers
88k views

Finding the PDF given the CDF

How can I find the PDF (probability density function) of a distribution given the CDF (cumulative distribution function)?

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