A distribution describing the time between events in a Poisson process; a continuous analogue of the geometric distribution.
Questions tagged [exponential-distribution]
681 questions
89
votes
5 answers
Relationship between poisson and exponential distribution
The waiting times for poisson distribution is an exponential distribution with parameter lambda. But I don't understand it. Poisson models the number of arrivals per unit of time for example. How is this related to exponential distribution? Lets say…
user862
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Why are survival times assumed to be exponentially distributed?
I am learning survival analysis from this post on UCLA IDRE and got tripped up at section 1.2.1. The tutorial says:
... if the survival times were known to be exponentially distributed, then the probability of observing a survival time ...
Why…
Haitao Du
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How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
In this current article in SCIENCE the following is being proposed:
Suppose you randomly divide 500 million in income among 10,000
people. There's only one way to give everyone an equal, 50,000 share.
So if you're doling out earnings randomly,…
vonjd
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32
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Outlier Detection on skewed Distributions
Under a classical definition of an outlier as a data point outide the 1.5* IQR from the upper or lower quartile, there is an assumption of a non-skewed distribution. For skewed distributions (Exponential, Poisson, Geometric, etc) is the best way to…
Eric
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From uniform distribution to exponential distribution and vice-versa
This is probably a trivial question, but my search has been fruitless so far, including this wikipedia article, and the "Compendium of Distributions" document.
If $X$ has a uniform distribution, does it mean that $e^X$ follows an exponential…
luchonacho
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24
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3 answers
How do I check if my data fits an exponential distribution?
How could I check if my data e.g. salary is from a continuous exponential distribution in R?
Here is histogram of my sample:
. Any help will be greatly appreciated!
stjudent
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Conditional expectation of exponential random variable
For a random variable $X\sim \text{Exp}(\lambda)$ ($\mathbb{E}[X] = \frac{1}{\lambda}$) I feel intuitively that $\mathbb{E}[X|X > x]$ should equal $x + \mathbb{E}[X]$ since by the memoryless property the distribution of $X|X > x$ is the same as that…
mchen
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18
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Suppose $Y_1, \dots, Y_n \overset{\text{iid}}{\sim} \text{Exp}(1)$. Show $\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1)$
What is the easiest way to see that the following statement is true?
Suppose $Y_1, \dots, Y_n \overset{\text{iid}}{\sim} \text{Exp}(1)$.
Show $\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1)$.
Note that $Y_{(1)} = \min\limits_{1 \leq i…
Clarinetist
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What is the PDF for the minimum difference between a random number and a set of random numbers
I have a list (lets call it $ \{L_N\} $) of N random numbers $R\in(0,1)$ (chosen from a uniform distribution). Next, I roll another random number from the same distribution (let's call this number "b").
Now I find the element in the list $ \{L_N\}…
Steven Sagona
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Distribution of sum of exponentials
Let $X_1$ and $X_2$ be independent and identically distributed exponential random variables with rate $\lambda$. Let $S_2 = X_1 + X_2$.
Q: Show that $S_2$ has PDF $f_{S_2}(x) = \lambda^2 x \text{e}^{-\lambda x},\, x\ge 0$.
Note that if events…
SecretAgentMan
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Mean of inverse exponential distribution
Given a random variable $Y = Exp(\lambda)$, what is the mean and variance of $G=\dfrac{1}{Y}$ ?
I look at the Inverse Gamma Distribution, but the mean and variance are only defined for $\alpha>1$ and $\alpha>2$ respectively...
Diogo Santos
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How to compare the mean of two samples whose data fits exponential distributions
I have two samples of data, a baseline sample, and a treatment sample.
The hypothesis is that the treatment sample has a higher mean than the baseline sample.
Both samples are exponential in shape. Since the data is rather large, I only have the…
Jonathan Dobbie
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Attainable correlations for exponential random variables
What is the range of attainable correlations for the pair of exponentially distributed random variables $X_1 \sim {\rm Exp}(\lambda_1)$ and $X_2 \sim {\rm Exp}(\lambda_2)$, where $\lambda_1, \lambda_2 > 0$ are the rate parameters?
QuantIbex
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How do you calculate the expectation of $\left(\sum_{i=1}^n {X_i} \right)^2$?
If $X_i$ is exponentially distributed $(i=1,...,n)$ with parameter $\lambda$ and $X_i$'s are mutually independent, what is the expectation of
$$ \left(\sum_{i=1}^n {X_i} \right)^2$$
in terms of $n$ and $\lambda$ and possibly other constants?
Note:…
Isaac
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Name for a distribution between exponential and gamma?
The density $$f(s)\propto \frac{s}{s+\alpha}e^{-s},\quad s > 0$$ where $\alpha \ge 0$ is a parameter, lives between the exponential ($\alpha=0$) and $\Gamma(2,1)$ ($\alpha \to \infty$) distributions. Just curious if this happens to be an example of…
nth
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