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

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Moment Generating Function of a nonlinear transformation of an exponential random variable

Let $\tau$ be an exponential random variable, with parameter $\lambda$. Let $$ V = \delta^\tau $$ where $0 < \delta <1$. Sorry if this notation seems strange, but it is what I am using, I ...
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21 views

polynomial regression model

I have 8 parameters with 3 levels and the number of tests required to study this case is 27. Can I generate polynomial regression model to describe interaction of these parameters?
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32 views

Finding transformation function for a distribution that looks like exponential

Suppose that we have two data sets, R and P. R is larger than or equal to ...
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20 views

Create a threshold for binary classification problem based on distribution of criterion

I created a criterion for my financial data-set for classify data to two classes for other processing (like neural network binary classificatio). After calculating ...
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2k views

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 ...
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29 views

Fitting an exponential distribution to data and finding third quartile problem

I have a data-set with range of 0 to 1. I'm fitting a distribution to it in MATLAB using ...
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39 views

Exponential distribution hypothesis testing

I want exponential distribution hypothesis testing with MATLAB. Is any test or method for that?
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26 views

likelihood problem with exponential distribution using R

How can I solve this problem using likelihood in R? The data below are the survival time (in years) for 10 patients over 65 years after the diagnosis of a particular type of cancer: 10.5 0.2 7.4 0.8 ...
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22 views

Would this be a problem that Survival Analysis can tackle? The problem deals with localized durations and uncensored data

I am trying to fit a model in R that doesn't have censoring. In other words, I know that each event will eventually happen. There are several experimental groups with people in each group receiving ...
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2answers
86 views

Which forecasting method for load profiles

I'm new to this forum and I'm quite new to forecasting. Currently I'm trying to learn the basics about exponential smoothing, ARIMA etc. Now I want to forecast the total energy consumption of a rather ...
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1answer
14 views

Given MTTF and Number of Items, how to calculate failing parts with Time?

I am wondering how to make use of MTTF Here is the situation, I am given an MTTF for an item type x and a certain demand for that item in the next 25 years, say 100 parts that will be in operation ...
2
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1answer
42 views

Rejection-Sampling of Exponential Distribution

Consider the following question. Consider the generation of random numbers following an exponential distribution with some known mean. Give three reasons why the rejection-acceptance method would ...
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2answers
65 views

Generate random number from a piecewise exponential distribution

I would like to generate a random number from a piecewise exponential distribution. I consider that the time-scale is divided in $J$ intervals with bounds $(s_{j-1},s_j]$, for $j=1,...,J$, and ...
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16 views

Markov Chain Queuing Problem

Suppose the times between successive arrivals of customers at a single-server station are independent random variables having common distribution $F$. Suppose when a customer arrives, he or she ...
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19 views

how does sd of empirical log survival function and empirical log survival function

a sample of size 100 from an exponential distribution with parameter lambda 1. In this case, I believe that standard deviation of the empirical log survival function is ...
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0answers
17 views

Weighing a variable based on distance to a known date

In a bankruptcy model, you want to assign a higher weight to a variable as a big event date approaches (such as a company's quarterly earnings announcement date) and you reverse this weighing as you ...
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0answers
37 views

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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0answers
9 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
24 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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1answer
72 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 ...
3
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1answer
211 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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38 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 ...
3
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1answer
49 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
60 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
29 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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24 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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25 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
59 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
53 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
103 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
87 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
36 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 ...
3
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1answer
122 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
66 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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50 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
79 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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57 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 ...
0
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1answer
78 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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82 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
106 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 ...
2
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1answer
123 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. ...
2
votes
1answer
84 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 ...
4
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2answers
166 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 ...
2
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1answer
62 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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1answer
51 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 ...
4
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1answer
319 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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48 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
531 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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54 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 ...