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

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2
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2answers
33 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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2answers
76 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 ...
0
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0answers
19 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 ...
-1
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1answer
24 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
votes
1answer
16 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
votes
1answer
63 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
votes
1answer
27 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 ...
5
votes
2answers
208 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 ...
1
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0answers
54 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
votes
1answer
37 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
votes
1answer
64 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
votes
2answers
198 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
votes
0answers
30 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?
1
vote
1answer
28 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
votes
0answers
37 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 ...
5
votes
3answers
48 views
0
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0answers
11 views

UMP test for two different distributions

My question: UMP test for H0: X~u(0,1) vs H1: X~Exp(1) My attempt : By nayman pearson lemma The best critical region is Y >= c Where Y has Irwin-Hall distribution (sum of uniform distribution) and c ...
1
vote
1answer
32 views

Equation for exponential function with covariate

I understand that the formula for an exponential relationship between X and Y can be written as follows: Y = a*exp(b*X) = exp(a+b*X) And from there, if I want to run as a standard regression, I would ...
1
vote
1answer
57 views

Expected lifetime of a device with two parts each having spares?

Consider a device with two parts : (1) and (2). Part (1) has 2 spares and part (2) has one spare. Lifetime of part (1) and its spares have iid exponential distribution with rate lambda. Lifetime of ...
2
votes
1answer
27 views

What is a tau parameter?

I am reading weight loss charts, they state "tau 146 days" and "tau 110 days". What is tau in this context? The charts are here: http://bit.ly/1xT253g
2
votes
1answer
104 views

How to evaluate R = max(X1,X2) - min(X1,X2)

How would you evaluate this if X1, X2 are independent exponentials? I know what $min(X1,X2)$ is and what $max(X1,X2)$ is. However, while $min(X1,X2)$ is exponential with parameter (lambda1 + lambda2) ...
2
votes
1answer
56 views

Exponential regression residual check

If you have an exponential regression of the form log(y) = b0 + b1x with predicted equation ลท = 10^(b0 + b1x) and you need to ...
0
votes
1answer
151 views

Unbiased estimator based on geometric mean for random sample on an exponential distribution

Let $X_1, \ldots, X_n$ be a random sample on an exponential distribution with mean $\theta$. Obtain an unbiased estimator for $\theta$ based on $G$, where $G$ is the geometric mean of the ...
2
votes
1answer
109 views

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 ...
0
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0answers
31 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?
0
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0answers
60 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 ...
0
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1answer
74 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 ...
28
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6answers
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 ...
5
votes
1answer
160 views

How to choose between exponential and gamma distributions

I have same data and I would like to choose a model for it. To start with I fit an exponential distribution and a gamma distribution. Now I wanted to do a simple likelihood ratio test . However, I ...
0
votes
1answer
78 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 ...
1
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2answers
217 views

Exponential distribution hypothesis testing

I want exponential distribution hypothesis testing with MATLAB. Is any test or method for that?
0
votes
0answers
31 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 ...
1
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0answers
23 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 ...
2
votes
2answers
101 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 ...
0
votes
1answer
36 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
votes
1answer
50 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 ...
3
votes
2answers
155 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 ...
0
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0answers
22 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 ...
0
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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 ...
1
vote
0answers
148 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 ...
0
votes
0answers
13 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 ...
0
votes
1answer
26 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 ...
3
votes
1answer
144 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
votes
1answer
1k 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 ...
0
votes
1answer
68 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
votes
1answer
68 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 * ...
1
vote
1answer
73 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 ...
2
votes
1answer
33 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 ...
0
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0answers
33 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 ...
1
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0answers
33 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 ...