# Questions tagged [cdf]

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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### Random variable without pdf but with a cdf?

In this video, the professor says that some random variables have no pdf but do have a cdf. Also, in my course material, I studied that converging in mean was stronger than converging in cdf which ...
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### Can't compute CDF for Inverse Gaussian distribution

I am trying to implement in Python the CDF of the Inverse Gaussian distribution: Inverse Gaussian pdf: $$f(x) = \sqrt{\frac{\lambda}{2\pi x^3}}e^{-\frac{\lambda(x-\mu)^2}{2\mu^2x}}$$ Inverse ...
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### How to estimate mean and variance for rate of change when I only have state data at different ages

I'll give you the intuition behind my problem first. I have data on whether children ($n \approx 200$) can read and their age in integers from 0 to 14. For each age, it is straightforward to ...
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### Why is CDF of binomial random variable step function

I just read that the cumulative distribution function for a binomial random variable is a "step function where the function is flat and then jumps at each nonnegative integer value". Can ...
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### Convergence in Distribution and Ordered Statistics [duplicate]

Let $X_1, X_2, \ldots$ be iid from Exp$(\theta)$ with density function $f(x) = \frac{1}{\theta}e^{-\frac{x}{\theta}}$. Find the limiting distribution of $M_n = Y_1 - \theta\ln(n)$ and $T_n = nY_n$, ...
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### Multivariate t-distribution CDF in python

Neither scipy nor statsmodels have multivariate t-distribution implemented. However, there are several code samples which implement Multivariate t-distribution PDF function, but I haven't seen any ...
1answer
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### same cdf equals same expectation?

So, if $X$ and $Y$ are both continuous random variables with the same cdf, does that mean that their expectations are the same? And the same thing in case $X$ and $Y$ are both discrete. Thanks in ...
1answer
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### R function to give me $P(X<x)$

I have this empirical discrete distribution with the respective percentiles (picture below). I want to know a R function which gives me $P(X\lt0.58)$ instead of $P(X\le 0.58)$ (given by ECDF function)....
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### Artifact in CDF with real data?

Looking for some help explaining why intuition is failing me in exploring this data. I've binned by dataset by a predictor variable to examine the response variable through CDF plots. I realize it may ...
0answers
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### Upper and lower limit of PDF

I have this example of a probability density function that is centered around 0. I would like to find out what are the lower and the upper limit of 95% of the data that is around 0. The goal is to ...
2answers
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### Do all random variables' probability distributions have entropy?

Entropy of probability distributions is the weighted average of the log probabilities of each observation of a random variable. Does this mean that every random variable that has a probability ...