The exponential tag has no wiki summary.
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1answer
29 views
Finding a probability mass function for $[x]$ is defined as the largest integer $n$ such that $n \leq x$
If $X$ is an exponential random variable with parameter $\lambda$ and we have that $[x]$ is defined as the largest integer $n$ such that $n \leq x$.
If $Y$ is defined as $$Y = \left[ X\over a ...
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1answer
51 views
What's a good transform for decaying function with a plateau
I have a dataset (y vs. t) that I think is best described by:
Slight initial downward slope
At maybe t = 1 or 2, steep downward slope
Asymptote at y = 0
I would like to transform the data so I ...
3
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1answer
128 views
Is the exponential distribution a good model for this data?
I'm trying to determine if the exponential distribution is a good model for a data set that I'm exploring. It doesn't have to be precise. I'm using the data for capacity planning (if it's a good fit) ...
3
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0answers
44 views
Likelihood analysis for exponential distribution
Assume a collection of independent exponential random variables $y_{1}, \ldots, y_{n}$ with means $\mu_{1}, \ldots, \mu_{n}$; where $\mu_{i} = \beta_{0}+\beta_{1}x_{i}$.
How can I find the profile ...
3
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1answer
56 views
Questions on likelihood analysis
Whilst studying likelihood methodologies, I've come across some results that I haven't been able to work out.
If $X$ and $Y$ are Poisson with means $\mu_{X}$ and $\mu_{Y}$, then the conditional ...
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0answers
78 views
How to handle negative Y values with exponential regression?
I have data points that include one instance of a negative y value. With this data, is it possible to generate a exponential decay function in a way that is mathematically sound? The only variable is ...
2
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1answer
115 views
Relationship between poisson and gamma
Supposing that I have an interval n units long with m arrivals, and I model arrival using a poisson distribution with lambda = m/n, it's pretty easy to show that the distance between successive ...
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1answer
40 views
Explain the distribution of these random variables?
Suppose I have 3 eggs, with independent hatching times (in minutes) following an $\text{Exp}(0.05)$ distribution, and A is defined as the earliest hatching time. If I were to plot A, how would I ...
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0answers
245 views
Hypothesis Testing on Exponential distributions
Let $X_1, \dots, X_n$ be independent exponential $(\theta)$ random variables. Suppose we are interested in testing $H_0: \theta = \theta_0 = 1$ versus $H_A: \theta = \theta_1>1$. Consider two tests ...
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64 views
Is there a closed form unbiased estimator of the median of n exponential variables from their mean? [closed]
Fix $n$. Suppose $T_1, \ldots, T_n \sim Exp(\lambda)$
For $n > 1$, is there ever an unbiased estimator of the median from a sample mean?
My attempt
$$\begin{align}P(median \le x) &= {K ...
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3answers
121 views
Discretizing Exponential distribution
I am working on a packet generator that can generate packets of 50 different sizes and the packet sizes follow exponential distribution. Given a mean packet size how can I choose the 50 packet sizes ...
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3answers
278 views
Exponential Distribution - Rate - Bayesian Prior?
I have gone through WinBugs documentation (for example, http://www.mrc-bsu.cam.ac.uk/bugs/thebugsbook/examples/html/Chapter-11-Specialised/Example-11_7_2-leukaemia.html). And also through this book ...
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0answers
50 views
Normally and exponentially distributed features
I have several features of which some are exponentially distributed and some are normally distributed.
Can I / should I used both at the same for training a classifier (e.g. neural net) and how ...
3
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2answers
263 views
Conditional expectation of exponential random variable
For a random variable $X\sim \text{Exp}(\lambda)$ ($\mathbb{E}[X] = \frac{1}{\lambda}$) I feel intuitively that $\mathbb{E}[X|X > x]$ should equal $x + \mathbb{E}[X]$ since by the memoryless ...
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1answer
37 views
Where does the $-u$ come from when working out $P(U > u)$?
The lifetime of a machine is modelled by an exponential random variable $X$ with $P(X>x) = e^{-\lambda x}, \lambda, x > 0$. This machine cannot be repaired. A maintenance crew checks this ...
2
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2answers
327 views
Poisson / exponential distribution
Next weekend you will be participating in 12km cross country race on a mountain.The average time between two successive wild animal sightings on the mountain is reported to be 5 minutes
(a) What is ...
0
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1answer
124 views
How to perform exponential regression with more than one predictors using R
Fitting exponential regression of form $y=ab^{x_1}c^{x_2}$
Here $x_1$ and $x_2$ are predictors and $y$ is dependent variable
how to calculate $a,b,c$ using R tool
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52 views
How to find a useful exponent for the pythagorean expectation?
I just read about the pythagorean expectation for baseball. For fun I am trying it out on other sports. I will start with the formula
...
2
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1answer
167 views
Conditional expectation conditional on exponential random variable
Given $X_1$, $X_2$ are independent EXP(1) random variables, how do I compute the following expectations:
$E[X_1 | X_1 + X_2]$
$P(X_1 > 3 | X_1 + X_2)$
$E[X_1 | ...
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0answers
84 views
About tail distribution of a sum
Do we know anything about the tail distribution of sum of squares of a limited number of i.i.d exponentially distributed random variables? I'm looking for a good bound.
8
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3answers
359 views
Parameter estimation of exponential distribution with biased sampling
I want to calculate the parameter $\lambda$ of the exponential distribution $e^{-\lambda x}$ from a sample population taken out of this distribution under biased conditions. As far as I know, for a ...
4
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2answers
125 views
Basic reproduction number
I'm not sure where to post this, so I thought I'd post it here. If there is another better place to ask this question then please could you let me know.
Let
$\beta$ = rate of infection, and ...
2
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1answer
121 views
How can I estimate parameters of a convolution of an exponential and gamma?
Ideally, I would input a one-dimensional array of data, and output the estimates for the three parameters. I'm not very familiar with any statistics software but I have MATLAB (and all of the free ...
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160 views
Using Stata for Survival Analysis with Exponential Model
Trying to:
Plot survival function estimates (by arm or treatment) as well as associated point-wise confidence intervals based on the Exponential
distribution
Compare the Kaplan-Meier curves with ...
2
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1answer
157 views
Understanding the exponential distribution
I'm trying to wrap my head around the Exponential distribution and the meaning of its parameter. The parameter is the rate, right? So take, e.g.,
$$X\sim \exp(0.05)\,.$$
Now the probability of failure ...
4
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1answer
186 views
Identify the parameters of the model $Y=\exp(\beta_0 + \beta_1 X + \beta_2 Z)+u_i$
I have the model $Y_i=\exp(\beta_0 + \beta_1 X_i +\beta_2 Z_i) + u_i$ where we assume $\mathbf{E}[u_i|X_i,Z_i]=0$ and $Var(X_i)>0,Var(Z_i)>0$, and I need to show that $\beta_0,\beta_1,\beta_2$ ...
2
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0answers
327 views
What is a second order exponential decay function?
Can you explain what is a second order exponential decay function:
$$
y(x) = y_0+A_{1}e^{-\frac{x}{t_1}}+A_{2}e^{-\frac{x}{t_2}}
$$
(the $t_i$, $A_i$, and $y_0$ are constants and, presumably, the ...
1
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1answer
200 views
“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 ...
-1
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1answer
165 views
How do I conduct peak detection for exponentially distributed data? [closed]
Which method would you recommend to detect peaks from an exponentially distributed data?
Knowing that the data source is a "page views" quantity over time, and considering the following histogram ...
10
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1answer
104 views
Correcting for normally distributed clock inprecision
I have an experiment which is executed on hundreds of computers distributed all over the world that measures the occurences of certain events. The events each depend on one another so I can order them ...
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154 views
Calculating Laplace–Stieltjes transform for general distributions
I am investigating exact and approximation methods to compute a Laplace–Stieltjes transform of various distributions. I know that it is easy for an exponential distribution, but I am confused for a ...
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1answer
173 views
Joint distribution of dependent exponential variables
I am trying to model a joint probability constraint of a union of correlated / uncorrelated exponential functions.
Formally, assume we have random variables $A_i \sim exp(\theta_i), \forall i \in ...
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1answer
91 views
Create a custom exponential function
I want to create a custom inverse exponential pdf with domain [0.00002, 0.0001] and range [0,1], where
x = 0.00002, y = 0 and
x = 0.0001, y = 1
The pdf should have the shape like that for a ...
4
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1answer
828 views
What is the expectation of exponential of the product of two random variables?
I am looking for examples of probability distributions that would allow me to characterize the distribution (at least approximately) and to compute the first two moments exactly of:
$$
e^{aXY}
$$
...
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1answer
205 views
Variance of exponential distribution when changing units
I was tutoring a Stat student taking a probability course and I came across a problem dealing with variance of exponential that has left me confused.
$X \sim \mathrm{Exp}(\mathrm{rate}=\lambda)$ so ...
2
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2answers
213 views
Arbitrariness of Euler's number in exponential of log-normal distribution
The Wikipedia article of the log-normal distribution says
If $X$ is a random variable with a normal distribution, then $Y = \exp(X)$
has a log-normal distribution; likewise, if $Y$ is
...
3
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3answers
539 views
Fitting an exponential mixture model with interval constraints on the mixture weights
What methods are there to fit a model of the form $y=A\mathrm e^{Bx}+C\mathrm e^{Dx}+E$?
Here is the actual scientific data to be fitted: http://dl.dropbox.com/u/39499990/Ben%2C%20real%20data.xlsx
...
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1answer
264 views
Conditional Expectation for Probability Distribution [duplicate]
Possible Duplicate:
How is the minimum of a set of random variables distributed?
I have two RVs from the same distribution (exponential distribution with parameter λ). How do I calculate ...
1
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1answer
140 views
Minimum of two exponential variates: What's wrong with this derivation?
Suppose we have $\newcommand{\E}{\mathrm{Exp}} X \sim \E(\lambda)$, $Y \sim \E(\mu)$, and $W = \min(X,Y)$.
I know that $W \sim \E(\lambda+\mu)$. I know how to derive it. But, I tried this alternate ...
3
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1answer
106 views
What distribution function $F$ is such that if $\{ X_i \}_{i=1}^{N} \sim F$, then $X_1 + … + X_N$ is most nearly exponential?
For what distribution $F$ is $X_1 + \dots + X_N$ most nearly exponential,
$X_i$ i.i.d. ~ $F$,
for $N$ = 2, 4, 8, 16 ?
How would one go about solving problems of this kind numerically ?
("Most nearly" ...
3
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1answer
227 views
Estimating Poisson waiting times: using the last, censored sample?
Assume I have a process that I assume to be Poisson, meaning that the waiting time between events is exponentially distributed. As a concrete example, assume I want to estimate the waiting time to a ...
0
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2answers
313 views
Problem with integrating exponential function in R
I'm trying to calculate the finite integral for the CDF of the normal distribution, when I plug the equation into Wolfram Alpha and integrate
exp((-t^2)/2) dt from -inf to 1000000
I get: 2.5 ...
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126 views
Posterior mean of exponential functions: how to do it with MCMC?
I am struggling with estimation of posterior mean of simple exponential function f(x)=exp(x). Mixing of the chain is quite good and there is no problem with estimation of simple mean, but since ...
3
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2answers
609 views
Exponential decay function
I have a model where I assumed a variable X would have an exponential decay over time t. I modeled it in R as
$$N = N_1e^{kt},$$
where $k < 0$ and $t$ is 1:95.
However, looking are some real ...
5
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2answers
365 views
Show series of exponential decay distributions in one chart
Every week we have new customers sign up, and some of them submit support requests. I'd like to graph the change in the number of support tickets per customer over time. I'm doing this by bucketing ...
3
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1answer
609 views
What reference can I cite for the proof that the sum of n exponential variables follows a gamma distribution?
There is a fairly common theorem, which states that:
The sum of $n$ independent variables following an exponential distribution $\mathrm{Exp}(\alpha)$ follow an gamma distribution $\mathrm{Gamma} (n, ...
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1answer
1k views
Finding expectation of reciprocal of sample mean
Consider the following distribution belonging to the exponential family.
$p_{\theta}(x) = \theta e^{-\theta x} $
The MLE estimating the $\theta$ parameter is
...
1
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1answer
287 views
Simulation of an exponentially distributed variable
A one-period jump diffusion model of a stock is the following: given the stock value at $T0$, $S(T0)$, the stock value at time $T$, $S(T) = S(T0)exp(x)exp(y)$. Given the inputs $m$, $s$, $pup$, ...
3
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1answer
419 views
Response variable with exponential distribution - how to analyse?
I would like to analyse the following data:
Number of observations: 430 trees
1 response variable: diameter growth of trees
2 categorical factors: tree species (9 levels) and treatment (2 levels)
...
6
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1answer
449 views
Order statistics (e.g., minimum) of infinite collection of chi-square variates?
This is my first time here, so please let me know if I can clarify my question in any way (incl. formatting, tags, etc.). (And hopefully I can edit later!) I tried to find references, and tried to ...
