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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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} &=& -...
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Probability of a 500 year flood occuring in the next 100 years - comparison of approaches

I'm looking at this problem A $500$-year flood is one that occurs once in every $500$ years. a) What is the probability of having at least $3$ such floods in $500$ years? b) What is the ...
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Suppose $\frac{1}{Y} \sim Exponential(\lambda)$, what is the pdf of Y? [on hold]

I am actually attempting to answer the following: Suppose $\Pr(X|Y=y) \sim \Gamma(a,y)$ and that $\frac{1}{Y} \sim Exponential(\lambda)$ What is $\mathbb{E}(X)$? However, I know that this is a ...
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Methodology to distinguish single and double exponential distribution

I have a set of n data points $x = [x_1, x_2,...,x_n]$ that follow an exponential distribution or a double exponential distribution (two different $\lambda$ parameters). In order to check which ...
71 views

How does an observation condition the next one, if the numbers are exp. distributued with uknown average?

We have a process that generates exponentially distributed random numbers, i.e., $P(X=x) = \lambda e^{-\lambda x}$. However, we don't know the value of $\lambda$. We observe the first realization with ...
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Testing for Constant Hazard Function

My colleagues and I have some unemployment data, and we'd like to test the hypothesis that it's drawn from a memoryless distribution (= constant hazard function). Is there a standard test for this? (...
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How to change exponential distribution into Normal distribution? [closed]

We have random data, which is exponentially distributed. Data = exp($\lambda$), where $\lambda$ = 0.5. If it is possible to change exponential distribution into the normal distribution. Then what ...
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Can the interarrival times of a continuous time markov chain be distributed with 2 parameter (scale,location) exponential distributions?

I'm trying to model data with a time-homogenous CTMC with a number of states with corresponding constant transition rates $\lambda_{i}$ when I notice that much of the transition times from one state ...
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Product of normal random variables and exponential random variables is exponential random variables?

How we can prove analytically, the Product of normal random variables and exponential random variables is exponential random variables?
166 views

What is distribution of $\sin(x)$? If x is exponential distribution

I am trying to find analytically the distribution of $\sin(x)$, If x belongs to an exponential distribution,
37 views

If the length of time the computer part lasts is exponentially distributed with mean value is $10$. So, for the exponential distribution, we can find the probability of one computer parts. $$p(x>... 1answer 67 views Show that nX_{(1)} is not consistent Consider a random sample from exponential distribution with mean \frac{1}{\theta}. I have to prove that nX_{(1)} is not consistent for \frac{1}{\theta} . A sufficient condition for consistency ... 2answers 84 views Alternating between two states {A, B} each with exp distributed durations. What's the probability of state=A at time t? Say I have a light bulb that can be on (A) or off (B). It alternates between being state A or B. It will be in state A for a duration a ~ exp(α), and in state B for duration b ~ exp(β), (... 2answers 125 views Conditional distribution of arrival times in Poisson process Suppose I know over a window [0, T) that I have observed n samples from a poisson process N_t \sim p(n|\lambda t) = \frac{1}{n!}(\lambda t)^{n}\exp(-\lambda t). What is the conditional ... 0answers 11 views How to compare two statistical distributions with unavailability measurements? I have two different measuring instruments to evaulate if an electronic device is working or not. These instruments provide a working/not-working reading each day and at the end of the month I compute ... 2answers 78 views Hypothesis test for composite null hypothesis of exponential parameter I'm having trouble defining the reject region based on the generalized likelihood ratio test. This is from a question of past exam I'm self-studying and still have the doubt, given that I got it wrong.... 1answer 37 views Re-scaling of exponentially distributed random numbers I am trying to generate M random numbers which are exponentially distributed and whose sum adds up to N (for simplicity, N=1). I found that the generated numbers are initially exponentially ... 0answers 21 views How to show the inter-arrival time variance of a Cox process driven by a stationary Poisson process of constant intensity \lambda is 3\lambda Ideas on how to show that the variance of a doubly-stochastic Poisson process(aka a Cox process) driven by a homogeneous(stationary) Poisson process of intensity \lambda is 3\lambda ? I've come ... 0answers 19 views Why knowing information about something doesn't help when it comes to Exponential Distribution? I've recently learned about Exponential Distribution and when it's appropriate to be used. There was the following example given. The duration of IC555 integrated circuits under normal operation ... 1answer 58 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 ... 0answers 18 views Questions regarding this derivation of the Poisson Distribution from exponential densities On page 217 - 218 of the pdf of this book, the author derives the Poisson Distribution using gamma and exponential densities. The author defines S_n to be the sum of a sequence of independent ... 0answers 20 views If there are covariant variables in the exponential distribution, how do I draw the QQ plot? Observation Data X=x,... x[n]； covariant variables are eta=eta,...,eta[n]. The parameters of exponential distribution are composed of covariant variables(eta) and lambda. So, X[i]<-rexp(eta[i]... 0answers 37 views To what distribution it's similar? Looks like an exponential but it's not To what distribution it's similar? Looks like an exponential but it's not. It's seems to have a property, that if I zoom it (xlim) then each time it has the same ... 2answers 125 views Can Kernel Density Estimation estimate an Exponential Distribution? Can Kernel Density Estimation estimate an Exponential Distribution? I tried to performed to make experiments with various kernels like: "gaussian" and "exponential", but performance seems to be very ... 2answers 378 views How do we build a confidence interval for the parameter of the exponential distribution? EDIT Let X_{1},X_{2},\ldots,X_{n} be a random sample whose distribution is given by \text{Exp}(\theta), where \theta is not known. Precisely, f(x|\theta) = (1/\theta)\exp(-x/\theta) Describe ... 1answer 86 views Why can't I write P(X>5|X>1) = P(X>5)? [duplicate] I have a confusion with the memorylessness property of exponential distribution. If exponential distribution is memoryless (i.e. the past has no bearing on its future behavior), why can't I write P(... 1answer 45 views exponential RV til bus arrives Suppose that you are waiting at a bus stop. The waiting time until a bus arrives is T where T is an exponentially distributed random variable with parameter λ i.e. P(T≤t)=1−e^{−λt}, ∀t≥0. (a) ... 1answer 46 views Geometric distribution described with rate parameter I don't understand this sentence from this paper (around equation 5): The function H(\tau) is the hazard function. H(\tau) = \frac{P_{\text{gap}}(g = \tau)}{\sum_{t=\tau}^{\infty} P_{\... 1answer 43 views What's the relationship between Pareto shape parameter (alpha) and exponential rate parameter (lambda)? I'm trying to do my undergraduate research on non parametric density estimation for a heavy tailed distribution. For that, I'm with a data set, which I assumed it should be Pareto distributed with ... 0answers 16 views Passion Distribution [closed] Suppose the number of tsunami in a season follows a Poisson distribution and the average number of tsunami that hit a region is 5 in every tsunami season A tsunami season lasts for 3 months. In the ... 0answers 15 views Exponential Test Given a collection of data points, without any other information I want to test for an exponential distribution. In a different case, I tested for normality using an Accord implementation of the ... 0answers 14 views Parameter estimation of exponentialy distributed variable with bounded observation I have data as below. I believe it is exponentialy distributed. But I could not observe the whole data, since I have limited time. The below table shows the monthly frequency. How can I estimate the ... 0answers 171 views Exponential distribution and Poisson process [duplicate] Could someone please explain to me what is exponential distribution and poisson process mean? How they are different and the relationship between them? [In simple terms]. Thanks 0answers 30 views 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 ... 2answers 78 views Estimator for \frac{1}{\lambda} using \min_i X_i when X_i are i.i.d \mathsf{Exp}(\lambda) Let X_1,\ldots,X_n be i.i.d. \mathsf{Exp}(\lambda) random variables, where \lambda is unknown. Consider f_{\min}(x) = \min_{i}(X_i)=  n \lambda  Exp(n\lambda x). I am told that \hat \... 0answers 108 views How do I calculate a Bayesian Posterior Distribution from an Exponential Prior and Sample Data I have a dataset where each observation is a length of time (e.g. 50 days, 70 days, 105 days) and I am trying to utilize Bayesian statistics to calculate a posterior distribution in light of new data. ... 1answer 75 views Proof for simulation of NHPP by thinning Background: I'm trying to show equivalency between the density function for a non-homogenous exponential process (NHEP?), (i.e. the arrival times of events generated by a non-homogenous Poisson ... 0answers 25 views Trouble understanding derivation of probability for continuous time markov chain I'm working on exercise 6.10 from "Introduction to probability models" by Sheldon M. Ross. There's an expression for the probability P_{00}(t) that I don't understand. Here's the relevant ... 1answer 212 views Minimal sufficient statistic for location exponential family Let X_1,\dots,X_n iid with pdf$$f(x|\theta)=e^{-(x-\theta)},\,\,\,\theta<x<\infty,\,\,\,-\infty<\theta<\infty.$$Part (b) of Problem 6.9 in Casella and Berger asks to find a minimal ... 1answer 164 views Expectation of standard exponential squared given sum of two standard exponentials So I have been working on this question for a while and made some progress , but I run into a problem about the normalizing constant. The question is, for X and Y i.i.d. standard exponential, find ... 0answers 21 views Explanation for Cumulative Distributive Function example I'd like to ask for clarification of the following example in my textbook. Example: Suppose events are occurring at random with average rate \lambda per unit of time. What is the probability ... 0answers 66 views Confidence interval with only one observation How could one create a 95% lower confidence interval for the expectation of a exponentially distributed r.v. with only one observation of the r.v., say 5555? 1answer 266 views CDF and MGF of a Sum of a discrete and continuous random variable I am currently dealing with the following exercise: Given the random variables X \sim Be(p), Y \sim Exp(\lambda), and assume they are independent. Set Z:= X + Y. Compute the Moment Generating ... 1answer 337 views The distribution of the product of a Bernoulli & an exponential random variable Let X be an exponential random variable f(x) = c e^{-c x} \text{ if }x > 0; 0 \text{ otherwise.} Let Z be a Bernoulli RV with Pr(Z=1)=0.45 and Pr(Z=0)=0.55. X and Z are independent. ... 2answers 213 views Prove convergence in distribution for n times the minimum of an unknown positive distribution Let Z_1, Z_2, ... be independent and identically distributed random variables with some density f. Suppose that P(Z_i > 0) = 1, and that$$ \lambda = \lim_{x\to 0} f(x) > 0$$Let X_n = ... 2answers 203 views Regression model when the dependent and independent variables show exponential distribution As the Title suggests i am trying to figure out what would be the regression model to use when both the dependent and independent variables show an exponential distribution. Do I have to perform a ... 0answers 120 views Can you have an exponential distribution where x is negative? [closed] I have a random variable with an exponential distribution and have solved an inequality to determine the maximum a posteriori rule (where if x > \alpha, I will choose hypothesis 1 over hypothesis ... 1answer 188 views How could “sum of exponential distribution is 1” be proven?$$f(x; \lambda) = \begin{cases} \lambda e^{-\lambda x} \quad \text { for } x \geq 0 \\ 0 \quad \quad \quad \text { for }x < 0\end{cases}  How can I prove that the sum of probabilities under ...
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}^{-...