# 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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### From Survival function to Cumulative density function (CDF), does CDF properties hold?

Given the following CDF values ...
2answers
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### Approximating non-integer median for CDF of discrete variable

In my googling, it seems the proper way to find the median of a cdf of a discrete variable is to stick to the discrete values provided, even if you overshoot and end up with an x where P(X <= x) &...
1answer
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### Proving sufficiency of properties of pdf/pmf [closed]

We have the following necessary and sufficient conditions for a pdf/pmf $f_X(x)$: $f_X(x)\geq 0$ for all $x$ $\sum_x f_X(x)=1$ if pmf or $\int_{-\infty}^\infty f_X(x)dx=1$ if pdf To prove necessity ...
1answer
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### Inverse of cumulative density function for Multivariate Normal Distribution

How do I calculate the inverse of the cumulative distribution function (CDF) of a multivariate normal distribution? Does it even exist for the multivariate case? I know this is possible for a ...
1answer
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### Which distribution creates an exponential-like pattern in x log scale?

I've been reading this very nice paper by Baltrunas et al. and I would like to have a distribution that looks as much as possible like the empirical data the authors found in the figure below: I don'...
0answers
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### Out-of-Specification for log-normal data

I want to calculate the Out-Of-Specification (OOS) probability of my dataset (probability of having a result which is greater than the acceptance limit). I have noticed that my results follow a log-...
1answer
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### Is $Z_t = U\sin(2\pi t) + V\cos(2\pi t)$ is strictly stationary?

Let $Z_t = U\sin(2\pi t) + V\cos(2\pi t)$, where $U$ and $V$ are independent random variables each with mean 0 and variance 1. Is $Z_t$ strictly stationary? Answer: I have proven that $Z_t$ is ...
3answers
60 views

### What information is required to aggregate percentiles

I have several thousand large datasets that are too big to fit into memory at once, so I need to keep them separate. It is easy enough to get the count, mean, std dev, min and max for the whole ...
1answer
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4answers
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0answers
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### Constructing portability density function by convolution of two PDFs and acquire ICDF

I need Gaussian-convoluted gamma distribution to fit my data, but the program I'm using doesn't allow construction of custom PDF. Let's call it pdf_g2. \mathrm{pdf_{g2}}(x,a,b,c,d) = conv[\mathrm{...
1answer
63 views

### Meaning of uniform percentile rank distribution?

I'm new to statistics and I've been following Think Stats 2. I've just gotten to Cumulative Distribution Functions. I have some questions regarding uniform distribution: What does it mean for the CDF ...