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

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Translate exponential distribution into normal distribution [on hold]

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
35 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
35 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
42 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
42 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
51 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
84 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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30 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
92 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
50 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
64 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
36 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
48 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 ...
1
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1answer
56 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?
3
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0answers
57 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
96 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: ...
2
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2answers
39 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
38 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
78 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
52 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
61 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 ...
0
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1answer
32 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
35 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
73 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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0answers
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
76 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 ...
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1answer
45 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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47 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 ...
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1answer
34 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
28 views
2
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44 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
164 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
43 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. ...
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2answers
74 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
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2answers
51 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?
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103 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
514 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
20 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
28 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
38 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: ...
3
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1answer
89 views

How to calculate the likelihood function

Lifetime of 3 electronic components are $X_{1} = 3, X_{2} = 1.5,$ and $X_{3} = 2.1$. THe random variables had been modeled as a random sample of size 3 from the exponential distribution with parameter ...
2
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1answer
31 views

Why are estimation results sharply different from the actual population (exponential distr.)

For my work, I analyze the field failure data sometimes and make decisions accordingly. (spare parts quantity, optimum preventive replacement point, ...) I made an experiment in Excel. Using inverse ...
8
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2answers
585 views

Outlier Detection on skewed Distributions

Under a classical definition of an outlier as a data point outide the 1.5* IQR from the upper or lower quartile, there is an assumption of a non-skewed distribution. For skewed distributions ...
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58 views

Help with an exponential function with an indicator and using the EM Algorithm

Two bulbs, Brand A and Brand B, in which their lifetimes are distributed exponentially with expectations $\lambda$ and $\mu$ respectively. They pair $X_i$ and $Y_i$. In the ith experiment, instead ...
2
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1answer
62 views

Maximum likelihood estimation from 2 exponentially distributed sample

$X_1,X_2,...,X_n$ and $Y_1,Y_2,...,Y_n$ are independent samples from the exponential distributions with parameters $\lambda$ and $\frac{1}{\lambda}$. What is the MLE for $\lambda$? I used the ...
3
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1answer
74 views

Guessing the length of a fish

I would like to solve the following excercise. Any help is appreciated. 90% of the fish in our pond are males, the rest are females. The length of the males are: $X+5$ inches, where $X\sim ...
7
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367 views

Expected value of a product of two compound Poisson processes

I'm working on my master thesis now and I've been struggling with a problem for some while now and no one seems to be able to help me or point me in any direction. So now I reach out to see if someone ...
2
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0answers
64 views

QQ plot for log-logistic and 2 parameter exponential in r

Is there any package in R, which help us to plot QQ plot for log logistic distribution and 2 parameter exponential distribution? What methodology can be adopted for the same?
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1answer
29 views

Is there a way to evaluate observations of exponentially-distributed variables, where some of the observations are still “alive”?

I am looking at the tenure (i.e. elapsed time between hire date and termination date) of various employees in a system. I want to test the hypothesis that two groups of employees have the same tenure ...
2
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0answers
44 views

Weighted density estimation of exponentially distributed RV

I am trying to get a weighted density estimation of some data. Unfortunately, the data is approximately exponentially distributed after the weight transform, which gives a false sense of positive ...