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

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Hierarchical process of exponentials

I'd like to work with a what I believe is a called a "hierarchical process" -- given by the multiplication of a pair of exponential distributions such that the random variable from one process is the ...
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2answers
63 views

Process with parameters that are themselves statistical

I'd like to work with a pair of statistical processes such that the random variable from one process is the parameter of the second process. The simplest case I can imagine (and which is still ...
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1answer
35 views

Finding the best fitted distribution for an experimental data with R

I have read most of the similar questions and answers, but still can not solve my problem... I have an experimental medical time-depending data, which I want to analyse and classify. I'm trying to ...
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2answers
53 views

Why is nls() giving me “singular gradient matrix at initial parameter estimates” errors?

I have some basic data on emission reductions and cost per car: ...
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0answers
40 views

Expected time in exponential distribution?

I'm using the exponential distribution to calculate a probability of an event to occur. $\lambda = 0.007$ failures/year. I am to calculate an expected time between 2 failures. My approach was to ...
2
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1answer
102 views

Central Limit Theorem for Exponential Distribution

I've spent so long, and I think I'm missing something super obvious. The question: Let $X_1,\ldots,X_5$ be five independent variables from the exponential distribution with mean $2$. Write the pdf ...
3
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1answer
40 views

Why is the exponential distribution chosen to model service time in Queuing theory?

Why is the exponential distribution chosen to model service time in Queuing theory ?
3
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1answer
30 views

Confidence interval for exponential distribution

Let $X_1,...,X_n$ random sample of $X$~$exp(\theta)$. i) Find a exact confidence interval for $\theta$ with coefficient of confidence equal to $\gamma$ ii)Find a asymptotic confidence ...
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2answers
376 views

What is my lambda here

The life of automobile voltage regulators has an exponential distribution with a mean life of six years. You purchase a six-year-old automobile, with a working voltage regulator and plan to own it for ...
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0answers
24 views

Adapt Kolmogorov-Smirnov Test to Lilliefors Test

I'm using EasyFit to fit distributions to a sample of data and test with the Kolmogorov-Smirnov test whether the null hypothesis may be rejected or not. But as this test estimates the parameters from ...
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1answer
23 views

Translate exponential distribution into normal distribution [closed]

I have a bunch of inventory management formulas that are supposed to be used with normal distributions, however my demand data fits an exponential distribution. Is there any way to translate the ...
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1answer
44 views

Heteroskedasticity- is everything over for my model?

So, I've got this exponential model: Which, when tested via Pagan- Breusch, got heteroskedasticity detected. Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant ...
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2answers
50 views

Exponential Regression to Forecast Future Growth

I need to use Exponential Regression to forecast the future earnings of a company. I have the past 10 years of quarterly data. I can do linear regression but the data is not in a linear fashion. ...
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3answers
62 views

Difference between rexp and qexp in R

I need to write a simulation that requires the use of exponential distribution. I was wondering what is the difference between the following two approaches in drawing random numbers from an ...
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1answer
49 views

Lower bound on the mean for an exponential distribution at a confidence level of 95%

for the life of me I simply cannot wrap my head around confidence intervals and upper/lower bounds on parameters. E.g $$ f(t;\tau) = \frac{1}{\tau} e^{-t/\tau}, \qquad t \geq0 $$ If $t=1$ (a single ...
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0answers
52 views

Show that MLE of $\lambda = \frac{n-T_n}{S_n+cT_n}$

$X_i$ are i.i.d exponential, mean $\lambda^{-1}$ for $1 \leq i \leq n$ and, the values are measured such that $X_i = c$ if $X_i \geq c$ and $X_i$ otherwise. Show that MLE of $\lambda = ...
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1answer
118 views

Understanding the mean and rate of an exponential distribution

Background: In the field of Civil Traffic Engineering the arrival of the vehicles in a road is random process modelled by exponential distribution [1]. Illustrative example: Along this line, let's ...
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0answers
41 views

Superposition of two renewal processes

Usually, superposition of two independent renewal processes may not lead to a renewal process. However, in my problem, the interval time between two events of the renewal process is more specific ...
4
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2answers
104 views

Linear graph turning exponential at a particular point

For a line graph, it behaves linearly upto a particular point and varies exponentially after it. Please suggest me a statistical approach/test to know this threshold point. When I plot a scatter ...
5
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1answer
52 views

Least squares with exponential model

I'm trying to fit values from this model $$y(x)=ae^{−bx}+c$$ where a, b and c are 3 different parameters that I want to find with least squares. So using least squares I want to find the value of a, ...
5
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2answers
94 views

Fit exponential distribution with noise

I'm trying to fit an exponential with noise (which in this case is a constant $c$) like this one $$ y(x) = \alpha e^{- \alpha x} + c \text{ ,}$$ having $(x_i, y_i)$ values (So $\alpha$ and $c$ are ...
4
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1answer
46 views

How to find maximum likelihood of multiple exponential distributions with different parameter values

Let's say that I have a bunch of independent samples, $X_1, X_2, \dots, X_n$ and that they all follow Exponential($\theta_i$) distributions. (So they all have pdf $f(x_i)=\theta_i\exp(-\theta_iy_i)$.) ...
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1answer
65 views

Poisson Process in R from exponential distribution

I am trying to simulate a poisson process sample path in R by starting off with exponentially distributed random variables. For example, for a value of $\lambda=0.5$, I can generate 500 samples and ...
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1answer
108 views

Large value of exp (B) in binary logistic regression SPSS what is wrong? [duplicate]

I had a very large value for Exp(B) in SPSS binary logistic regression. What is wrong and what should I do?
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74 views

How to fit an exponential equation of the form $Y = A + Be^{CX}$ to data

I need some assistance with a nonlinear adjust. I am trying to make a mathematical model that describes the rate of silicic acid escaping from an underwater sediment. For theoretical reasons, the ...
2
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2answers
106 views

Why do I get linear model when I tried to fit exponential model?

I was wondering why do I get linear model when I'm using exponential model, y = a * exp(-b*-x), to fit my data. Here is my code: ...
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2answers
49 views

Variance of a function of the sample variance

I'm looking for the sampling standard deviation of $\hat\sigma^\gamma$, where $\hat\sigma$ is a sample standard deviation. For simplicity, lets do the sample variance of the sample variance and take ...
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0answers
58 views

Expected value of a function of an exponential random variable

I want to find the expected value of a non-decreasing cost function $c$ of an exponentially distributed random variable $X$ with mean $a$. Considering some constant $t$, the expected value that I ...
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0answers
151 views

How to fit a two phase exponential decay curve?

I have a model where the variable y theoretically should have an exponential decay over time x. The real data showed a fast decay to begin with and a slower decay towards the end. Here is the code: ...
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0answers
54 views

Probability distribution of functions of random variables

A system will function as long as at least one of three components functions. When all three components are functioning, the distribution of the life of each is exponential with parameter ...
2
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1answer
65 views

probability distribution of the maximum

Let T be a random variable giving the time to failure of led lights that follow exponential distribution with a mean value of 15 000 hours. We put three new lights at the same time. Find the ...
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1answer
35 views

How to compare s shaped curves?

I have two variables A and B that can take positive values, they are two different counters of "votes" for a group of about 400 individuals. My hypothesis is that these two kind of votes are related ...
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0answers
38 views

Likelihood of a Poisson-described event to occur in the next second

Consider a recurring event for which the time periods between consecutive events is exponentially distributed. For argument's sake, I'm waiting for a taxi on a busy street. How might one calculate the ...
3
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2answers
88 views

Detecting if samples belong to a given distribution

I am a networking person and I am trying to use statistical methods for a problem I am facing, so I would appreciate any help or pointers. I have users that access the medium, but in case 2 or more ...
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25 views

Exponential distribution for lightbulbs

The lifetime of a certain type of a lightbulb is 20 months. If a household has 12 light fixtures whose lightbulbs are replaced at the same time. Determine the probability that 5 of the lightbulbs will ...
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1answer
100 views

generate random exponentially distributed X data between zero and a max value [closed]

For my work issues, I need to generate random exponential distributed X data between zero and a max value. In my specific case range is (0,750) I know about inverse distribution function (IDF) for ...
0
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1answer
50 views

Exponential distribution of the time between recurrences

Patients in a hospital are treated for certain illness. The time in days that no recurrence takes place follows exponential distribution with mean of $\theta = 27$ days. The following table gives the ...
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0answers
61 views

How to find P(X = Min(X,Y)) for an exponentially distributed function?

Assuming $X$ and $Y$ are independent, and each of them have their own parameters $A$ and $B$, how do I find $P(X = \min(X,Y))$ for an exponentially distributed function? I understand that ...
0
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1answer
38 views

Non-Linear regression that captures jumps and an exponential decay

I have some data that has the pattern in the picture below (but little noisier than that). I want to run a non-linear regression that tries to capture the dynamic of this data in the time-series ...
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1answer
31 views
2
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1answer
59 views

Normal distribution area vs. exponential distribution area

Why is the area to the left of the mean different in normal distributions comparatively to exponential distributions? I understand that in normal distributions area is allocated symmetrically on ...
5
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1answer
166 views

What is the limiting distribution of exponential variates modulo 1?

I have tried to find the limiting distribution of $X_n\sim\text{Exponential}(\lambda/n)$ by finding the cdf and taking the limit. I got: \begin{align*} F_{X_n}(X)) = \int_{0}^{X} \frac{\lambda}{n} ...
2
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1answer
63 views

Exponential equation fitting

I have two variables: y= head (0.5,0.10,0.15,0.25,0.34) and x= instar (1, 2, 3, 4,5). How fitting my data on exponential growth in R? I need p-value fitting, F (is possible?), R^2 and degree freedom. ...
0
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2answers
88 views

Model for exponential decay with lots of zeros

I am trying to test for the effect of a treatment on a response variable. The response variable decays over time in what I believe is an exponential way. The measurement doesn't go below zero, so ...
3
votes
2answers
58 views

Distribution of the exponential of a mixture?

Suppose that $X$ is distributed as a finite mixture of normals $$\sum_{j=1}^k w_j \phi(x;\mu_j,\sigma_j^2).$$ Is $\exp(X)$ distributed as a finite mixture of log-normal distributions?
5
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131 views

Test if 2 exponentially distributed datasets are different

I have 2 exponentially distributed datasets and I want to be sure that they are from different distributions. Unfortunately a necessary error in the detection of the data forces me to discard all data ...
6
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4answers
691 views

What are the formulas for exponential, logarithmic, and polynomial trendlines?

In creating linear trendline, I used the following formulas: $$y=mx+b$$ $$m = \frac{n\sum(xy)-\sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y- m \sum x}{n}$$ and this for the R-squared: ...
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0answers
22 views

Is it possible to incorporate on/off cycles into a product's failure rate prediction along with its field failure rate and test data?

If I have a electronic module whose failure rate I am calculating using the chiinv() function in Excel, and the following data available to me: -test failures and test hours for the module and the ...
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1answer
30 views

Estimator $\gamma = \sum a_i\times x_i$ , where $X_i \sim \exp(t_i \theta )$ Show $\gamma$ is unbiased if $\sum a_i/t_i = 1$

I'm getting really confused with the estimators in this question! $X_i \sim \exp(t_i \theta x)$ where $t_i$ are positive constants. The MLE for $\theta = \frac n{\sum t_i x_i}$ And $\phi = ...
3
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1answer
55 views

For the survival analysis package in R, what is the log-likelihood of “survreg( Surv(time, censor) ~ age, dist=”exponential“)”?

I am currently trying to read through examples from http://www.ats.ucla.edu/stat/r/examples/asa/asa_ch1_r.htm. One of the models I saw was: ...