# Questions tagged [exponential-distribution]

A distribution describing the time between events in a Poisson process; a continuous analogue of the geometric distribution.

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### Deriving the PDF of an exponentially modified Gaussian RV

For a random variable $Z = X + Y$, where $X$ is an exponential RV with $λ = 1$ and $Y$ is a Gaussian (Normal) random variable with mean $μ$ and standard deviation $σ$, how could we derive the ...
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### rpart with survival data: what do the reported rates mean?

This is essentially the same question as this one but the accepted answer doesn't answer it. I made data consisting of three groups, each following an exponential distribution with rates 1, 3 and 6 ...
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### Probability of service in a queue theory problem with exponential random variable

I have one queue with two servers $S_1$ and $S_2$.The serving times are modeled $\sim exp(\mu_1)$ and $\sim exp(\mu_2)$ respectively. The first server is free while the second has two clients, $A$ ...
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### Probability of being still in the system in a queue system

I have one queue with two servers $S_1$ and $S_2$.The serving times are modeled $\sim exp(\mu_1)$ and $\sim exp(\mu_2)$ respectively. The first server is free while the second has two clients, $A$ ...
76 views

### Binomial and exponential distribution

If I am given $N$ is from a binomial distribution with the parameter $n,p$ and also $X$ is from exponential distribution with the parameter $\lambda$. Assume that $S_N=X_1+X_2+...+X_N$. How can I find ...
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### Exponential distribution and gamma prior

I want to use Bayesian conjugate to update my prior. Let's say I model bus arrivals by Exponential distribution with lamba=0.5. It means on average I will wait for <...
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### Poisson process - time of arrival of a client, given that one client arrived at first interval

I have the following situation: I have a Poisson Process with $λ=7$ (seven customers / hour). This process describes the arrival of customers in a store. The store is open from 9:00 AM to 19:00 PM. My ...
150 views

### Mann-Whitney-U for exponential distributions?

I have two distributions, that look like the following: They appear to be exponential and have different sample sizes (369 vs 60). I would like to do some hypothesis testing. I know that I can use ...
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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 $\Gamma(2,1)$ ($\alpha \to \infty$) ...
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### Exponential Distribution problem with many items to be tested

I have the next exercise: The duration time X, in months, of a type of electrical resistance has the next probability density function: Then if 10 electrical resistors are tested, what is the ...
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### How to find a good estimator for $\lambda$ in exponential distibution?

I have an Exponential distribution with $\lambda$ as a parameter. How can I find a good estimator for lambda?
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### Two sample test for exponential distribution with only two observations

Suppose we have two independent random variables $X_1 \sim \exp(\lambda_1)$ and $X_2 \sim \exp(\lambda_2)$ . Now, we are given just one observation each from the two distributions above, say $S_1$ and ...
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### How to test if a process is poisson, if there are a lot of zeros

I have foot traffic data for how many people entered a building for every hour, for several days. This SOUNDS like it should follow a poisson process. Problem: I need to statistically confirm that my ...
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### Statistical power of the Lilliefors test: how to compare results for samples of different sizes?

The power of the Lilliefors test (LT) strongly depends on the sample size. I need to apply LT to a discrete distribution to find the minimum value m_min above which it is exponential. I need to do it ...
I am trying to generate a synthetic earthquake database where the number of events ($N$) with magnitude ($M$) in the range $[M, M+\delta_M]$ follows: $\log_{10}(N) = a - bM$ where $a$ and $b$ are ...