Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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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Intuitive explanation of $\Pr(X_1 < X_2 \mid \max(X_1, X_2, X_3) = X_3)$ where $X_1, X_2, X_3$ are exponentials

Let $X_1, X_2, X_3$ be exponential random variables with rates $\lambda_1, \lambda_2, \lambda_3$. We have the following $$\Pr(X_1 < X_2 \mid \max(X_1, X_2, X_3) = X_3) = \frac{\lambda_1 + \lambda_3}{\lambda_1 + \lambda_2 + 2 \lambda_3}$$ Which I…
MT_
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modeling time between calls with exponential distribution

I've read that time between calls (in a call center) can be modeled with exponential distribution. My question is this: the shape of the exponential distribution has a decreasing nature. Suppose that there are 6 calls at average in an hour. In this…
Sanyo Mn
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How to computed "truncated shifted exponential distribution"?

I have a research problem to solve. For regular exponential distribution, $$F(z|\lambda)=\begin{cases}0\;\;\;\;\text{if }z<0\\1-e^{-\lambda z}\;\;\;\;\text{ if }z\geq 0\end{cases}$$ with density $$f(z|\lambda)=\begin{cases}0\;\;\;\;\text{ if…
Ludwig Gershwin
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Prove that the sum of exponential random variables is a gamma distribution

I tried to prove using the convulution approach but it didn't work
user324997
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"Exponential" distribution with negative scale parameter?

The standard exponential density is only defined for $x>0$ and scale parameter $\lambda > 0$ where the density is given by $f(x) = 1/ \lambda * exp(-x/ \lambda)$. My question is, does a similar density where $\lambda < 0$ and $x < 0$ make any sense…
felix
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Probability that one of two exponential random variables is the smaller

Let $X_1 \sim \text{exp} \left( {\lambda}_1 \right)$ & $X_2 \sim \text{exp} \left( {\lambda}_2 \right)$, and they are independent. Now consider the random variable $Y = \min \left[X_1, X_2 \right]$. I need to estimate the $\mathbb{P} \left[Y = X_1…
Brian Smith
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How to compute expectation of a exponentially distributed variable given the value of another variable?

I have 2 mutually independent random variables: $s$ is distributed exponentially with parameter $\lambda$: $s\sim F(\cdot|\lambda)$ $\epsilon_x$ is distributed exponentially with parameter $\chi$: $\epsilon_x\sim F(\cdot|\chi)$ Define $x\equiv…
Ludwig Gershwin
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Why do we associate the negative symbol in the exponent of $e^{- \theta y}$ to $T(y) = -y$ rather than $c(\theta) = \theta$?

I am currently trying to learn about the exponential family of distributions. I have the example $Y \sim \exp(\lambda)$, where the density is $f_\theta (y) = \theta e^{- \theta y}$ for $y \ge 0$ and $\theta > 0$. Here, we have that…
The Pointer
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Prove $Y_2 - (Y_1 - 1)^2/2$ is an $Exp(1)$ random variable

I am studying Monte Carlo simulation and I came across with this claim from notes: Let $Y_1$ and $Y_2$ be two independent $Exp(1)$ random variables. We accept $Y_1$ as one sample when $Y_2$ is larger than $(Y_1 - 1)^2/2$. Then by the memory-less…
Van Tom
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conditional distribution in coin tossing problem

Let $X$ and $Y$ be exponential random variables with parameters 1 and 2. A coin has probability of getting heads as $p$ and probability of getting tails as $1-p$. Let $Z$ be another random variable such that $Z=X$, if the coin turns heads and $Z=Y$,…
Nisha
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Find lambda for exponential distribution

I'm trying to find the function which allows me to find lambda if: $$y = 1-e^{-\lambda x}\,.$$ I tried doing this by: \begin{eqnarray} y-1 &=& -e^{-\lambda x}\\ e^{-\lambda x} &=& -(y-1)\\ -\lambda x &=& \ln(-(y-1))\\ -\lambda &=& (\ln(-(y-1))) /…
Alesi Rowland
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Alternative heavy right tailed distribution to exponential distribution

I have data whose distribution resembles an exponential distribution, but the data has a heavier tail than the exponential distribution. I will be very glad for any recommendation of an alternative to the exponential distribution for the data.
oercim
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Exercise about exponential distribution

My textbook has this exercise, in the section regarding exponential distribution: Given an arrival process with $\lambda = 8.0$, what is the probability that an arrival occurs in the first $t = 7$ time units? I used this formula: $F(t)=1-e^{-λt}$ To…
alkazam
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Can I use the exponential distribution to model data with some negative values?

my data ranges between x=(-10, 60). X represents energy savings after adopting an energy efficient product, where most individuals save energy (positive x) but a few use more energy (such as through the well-documented "rebound effect"). I think…
Blake Shurtz
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Can you have an exponential distribution where x is negative?

I have a random variable with an exponential distribution and have solved an inequality to determine the maximum a posteriori rule (where if $x > \alpha$, I will choose hypothesis 1 over hypothesis 2). I doubt my finding, however, because the value…
vintagedeek
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