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

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fitting an exponential decay onto a regression line

I have data for adherence to medicines which follows a downward linear trend for about 6 months (from 100%) and then plateaus at about 50%. Another way of describing it is by saying that adherence ...
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8 views

Accounting for minimum dependent measure in data when fitting a distribution

I have what is possible a naive question. I am current comparing various models (i.e. distributions). And the comparisons do not involve different distributions but rather how the model is fed the ...
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1answer
21 views

Random number from exponential distribution with a scale parameter

I have been using $r = \mu \ln(1 - n)$ to obtain pseudo-random numbers from an exponential distribution, where $\mu$ is the distribution mean and $n$ is a pseudo-random number from 0 to 1. Now I want ...
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45 views

Rescaling exponentially distributed variables before clustering?

I want to cluster data that contains binary variables, exponentially distributed (power law) variables, and normally distributed variables. I'm considering preprocessing the data in the following way ...
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1answer
133 views

Bias of the maximum likelihood estimator of an exponential distribution

The maximum likelihood estimator of an exponential distribution $f(x, \lambda) = \lambda e^{-\lambda x}$ is $\lambda_{MLE} = \frac {n} {\sum x_i}$; I know how to derive that by find the derivative of ...
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35 views

Obtain the coordinates of one point (X1,Y1) where it is maximum the change of the curve

Dear community, I used a figure obtained from internet to illustrate what I would like to solve. Imagine this exponential regression curve. How can I get the exact point of the curve where it is ...
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1answer
42 views

Confidence interval for the “shift parameter” of a non-central exponential distribution

Suppose that $X_1, X_2, \ldots, X_n$ (with $n > 0$) is a random sample from a non-central exponential distribution with probability density function: $$f(x | \lambda, k) = \lambda * ...
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1answer
50 views

Maximum likelihood estimation for a sequence of observations

Assuming $A_1, A_2, \ldots, A_n$ are independent exponential random variables (each having the same parameter and, for the sake of simplicity, let's assume the value of the parameter is 1). Define ...
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1answer
28 views

Variance regarding to the exponential of uniform distribution

If X has a uniform distribution of [0,1], and f(x) = e^X and g(x)=2^X. I generated 1000 values for X and applied to both two functions. And I calculated the variance after the transformation. The ...
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23 views

Exponential Distribution Data

The life time of a bulb follows exponential distribution. Such types of examples frequently occurs in many areas of science and engineering. Is there any source of practical data set of two ...
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19 views

P(no collision) with Poisson arrivals and exponential packet length

The Aloha scheme is a time-division multiple random access scheme used in networking, developed at the University of Hawaii by Norm Abrahamson for their network, ALOHAnet to deal with the fact that it ...
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1answer
48 views

dealing with exponentials in python - infinities and overflows [duplicate]

In a machine learning algorithm that I'm using, I need to get the exponential values of something in one of the steps. This is the step that I'm dealing with right now: I've already got all the ...
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33 views

Self Study Qn on Exponential Distribution

I am currently working on a self-study question relating to exponential distribution. I made an attempt but was not able to make sense of the answer. When I looked up the reference guide, it offered ...
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1answer
45 views

the Poisson result and Exponential interpretation for spare part requirement analysis

I am confused with with the Poisson result and Exponential interpretation for spare part requirement analysis. I try to calculate the required number of spare parts for a disposable remove-replace ...
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2answers
99 views

Exponential distribution probability

Let X and Y be independent random variables such that $X∼Exp(1)$ and $Y∼Exp(2)$. Find the probability that $3X+4Y≤5$. I thought the equation for solving this was the integral from $\int_0^a \int_ ...
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3answers
81 views

Question on Exponential Distribution

I have a question on the exponential distribution: Question The waiting time to receive food after placing an order at the local sandwich shop follows an exponential distribution with a mean of ...
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1answer
35 views

Exponential Distribution Expected Value

Question 1 (part 1) I was attempting to use the exponential distribution to solve the following problem: the time between cars passing on a road can be modelled with an avg rate of 3.5 cars per ...
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1answer
113 views

Exponential Distribution PDF: Why multiply by lambda?

Hoping you can help me understand the probability density function for the exponential distribution. Given that the distribution's PDF is described as follows when x > 0: $$\lambda e^{-\lambda x}$$ ...
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1answer
58 views

When to use CDF and PDF for Exponential Distribution [duplicate]

I am doing a self-study on Exponential Distribution and noted an exponential on my text giving that: CDF of Exponential Distribution $$ F(x) = 1 - e^{-λx} , $$ PDF of Exponential Distribution $$ f(x) ...
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36 views

Determining the uncertainty of an exponential fit

My problem should probably be built up from the beginning, so lets start there. I performed a certain experiment 25 times. Every time, the experiment consists of 5000 measurements, and each ...
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1answer
56 views

Consistency of an order statistic in exponential distribution

I have two questions. 1) If $X_1,X_2,X_3,...,X_n$ constitute a random sample of size $n$ from an exponential distribution, show that $\bar X$ is a consistent estimator of the parameter $\lambda$. ...
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56 views

Kolmogorov-Smirnov test for large sample [duplicate]

I am investigating if an exponential distribution is a good fit for a large sample of data (200) I have. I have already looked at a histogram but was wanting to investigate further. I was going to use ...
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1answer
67 views

Applying Spearman's rank correlation on average values, does it make sense?

I have a sample of 2000 projects randomly extracted from a population of 10,000,000 following an exponential distribution. From this sample I would like to check if a statistical dependency exists ...
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66 views

Total waiting time at a server with exponential arrival times

Question: In a certain system, a customer must first be served by server 1 and then by server 2. The service time at server $i$ is exponential with rate $\mu_i$, $i = 1, 2$. An arrival finding server ...
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1answer
95 views

Obtaining a Probability Distribution From a Survival Function

Edit: I basically want to have a probability curve where a X value of 0.002 would be associated with a Probability of 1 and would also have data points of (0.005,0.1), (0.008,0) which is seen in the ...
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1answer
107 views

How to define weights when testing an exponential trend?

In a linear model including ANOVA one can test a trend (e.g., linearity, quadratic effect, etc.) among the ordered effects (regression coefficients or factor levels) through assigning proper weights. ...
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53 views

Geometric mean of uniform variables

I am doing some independent study in asymptotic statistics and point estimation and am aware that you can get from log transformations of uniform random variables (exponential) all the way up to ...
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149 views

Maximum Likelihood Estimator of the exponential function parameter based on Order Statistics

The following question is part (1/4) of a 2.30h written exam for the course "Probability and Statistics" in a school of engineering. So, although tricky and difficult (because the Professor is really ...
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1answer
50 views

Calculating a marginal distribution for the joint density distribution of an exponential distribution with a rate given by a Gamma distribution

This is a follow-up question from one I asked over at MathOverflow: http://mathoverflow.net/questions/158806/is-there-a-simple-closed-form-solution-for-the-joint-density-distribution-of-an The ...
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46 views

NIST exponential smoothing formula

I am trying to relate data and results in NIST website with the formula defined in previous page from the same website. But I am missing something here: Does initial trend & season indices ...
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1answer
207 views

Holt-Winters exponential smoothing formula

I am trying to implement Holt-Winters exponential smoothing in Java program (I understand that R and Python have implementations of these algorithms, but I can't use those due to other reasons, so ...
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40 views

How to set initial values for Holt-Winters backcasting?

I'm trying to figure out how to set initial seasonal values for backcasting of the multiplicative Holt Winters. As pointed out in this thread: Holt Winters initialization using backcasting like SPSS, ...
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2answers
366 views

Manually fitting a mixture distribution in matlab

I am trying to fit a mixture model containing a gamma and an exponential distribution: The general form, using the pdfs, is: p * gammapdf + (1-p) * exponentialpdf. The pdfs for the Gamma and ...
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42 views

How to select the exponential decay constant for weighting in proc logistic?

I am trying to predict the sales conversion using proc logistics in SAS. Right now I have around 3 months of data, and it will gradually grow to more than an year over time. My intuition is that the ...
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1answer
165 views

Variance of arrival process with shifted exponential distribution

Here we have a arrival process. The inter-arrival time follows a shifted negative exponential distribution. The density function of the distribution is: $$f(t)=\lambda ...
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22 views

How to use Kullback–Leibler divergence to help me choose the best distribution function?

I am now using Exponential distribution to model the the time intervals of a sequence of random events.Since I can choose several different lamdas for this model , I want to find out which lamda of ...
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1answer
90 views

Exponential Distribution, Poisson process

I have a question relating to Poisson which I would like to get some advice on. I am doing this on a self-help exercise, but unfortunately it doesn't provide answers for me to verify. Basically in ...
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1answer
32 views

exponential approximation at adaboost

I am reading about AdaBoost algorithm, I cannot understand (7). How can it be like this? If you want full document, you can get it at http://cseweb.ucsd.edu/classes/fa01/cse291/AdaBoost.pdf ...
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50 views

exponential EWMA- statistical process control to monitor time between events

I am looking into control charts to monitor time between events for rare events. A quick literature review revealed that the following four methods are worth investigating: Cumulative Count of ...
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1answer
43 views

Quick Problem with maximizing profit using different distributions

I need a little help with a problem I am working on. So here's the situation, a seller can produce a apple for $1.00$ and I need to find the optimal price of selling the apple and expected profit per ...
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1answer
29 views

How would I assign the optimal weight matrix to combine the following moment conditions in MM?

The following information is given: Based on a sample x(n), with n = 1,..., 100 from the exponential distribution, we want to estimate lambda but the original data was lost; we only know that 38 ...
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42 views

Exponentially weighted average of data stream variance

For modeling a sequence of data, I once heard the technical term of "exponentially weighted average of the data stream variance". It is defined recursively as I am not clear why does this recursive ...
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33 views

Exponential Service Times when Minimum Service Time is Reasonable in Queuing Theory

I asked this question on the Mathematics stack exchange site but I didn't get a response. If posting it here means it should be closed or migrated from there, is there a way that i can do that? Or can ...
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168 views

Exponential Service Times When a Minimum Service Time is Reasonable

In many queuing models it is assumed that the service time follows an exponential distribution with parameter $\mu=1/\lambda$, where $\lambda$ is the average rate of service. An example might be a ...
2
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1answer
119 views

What is the parameterization of exponential distribution for survival in Stata?

I'm new to data analysis so this is kind of a simple question. I would like to understand why I cannot reproduce a survival curve generated by a fitted exponential model from Stata. I use the ...
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1answer
47 views

Picking the smallest number of i. i. d. exponential variables to satisfy a condition

The lifetime of a brand of lamp is exponentially distributed with parameter $\lambda=0.01\;h^{-1}$. How many lamps are needed so that there's a 95% probability that a room is lit for 1,000 hours, if ...
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1answer
88 views

Confusion on the relationship between laplace distribution and exponential distribution

If $X \sim Laplace(\mu, b)$ and $\mu = 0$ such that $X \sim Laplace(0,b)$, it becomes a form of the exponential family. Unfortunately, one source tells me that it becomes $|X| \sim exponential(b)$, ...
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56 views

calculate the bias and variance of the MLE in an exponential family

I'm trying to calculate the bias and variance of $\hat{\lambda}_{MLE}$ where $X \sim exponential(\lambda)$. Secondly, does it attain the CRLB? Attempt: $$f_x(X) = \lambda e^{-\lambda x}$$ ...
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2answers
95 views

Poisson and Exponential Distribution- Is the following question correct?

Accidents occur with a Poisson distribution at an average of 4 per week. i.e., $\lambda= 4$. Calculate the probability of more than 5 accidents in any one week. What is the probability that at least ...
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1answer
242 views

Goodness of fit test for exponential distribution

The given data below shows the time in intervals in seconds between successive white cars in flowing traffic in an open road.Can these be modeled by an exponential distribution. ...