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# Questions tagged [exponential]

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

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23 views

### Exponential regression fit overestimates

I have a non-linear data set that I used to fit an hyperbolic curve of the following format: $$q = \frac{q_i}{(1+bD_it)^{1/b}}$$ $t$ is the x-axis (independent variable), $q$ is the y-axis (...
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### Why Are they doing exponential distributions?

With many thanks for help in why my exercise is using a Gamma distribution, I am still confused by another part. The plot: The commentary: We may suspect from the above that there is some sort of ...
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### how to use depended / non-random observations when trying to inference exponential parameter

consider this case: There is a price rate for a certain product that changes throw time, The price rate is changed every x minutes (unknown, not constant). This price has depended / non-random ...
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### Exponential random on clustered graphs

In, short am using time use data and I am aiming to represent the way everyday activities connect in time and space. So i created the above graph in Gephi. The nodes are activities and edges are 2nd ...
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### How should I go about doing regression with a series of exponents involved?

I have a table of data with input values and target values, and I was tasked to do something quite peculiar. I was tasked to run a sort of exponential regression and report back with the coefficients ...
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### What statistical test is suitable for testing the goodness of fit for an exponential regression model?

I want to do a study about the risk factors of heart failure disease that will affect the survival time of a patient. My independent variables: age, smoking status, ejection fraction etc.., and my ...
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### Statistical specification for a Regression with continuous finite range count like data

I am interested in explaining what kind of personal characteristics and work environment variables are associated with sickness absenteeism. My dependent variable is the total number of days a given ...
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### Back transforming the intercept of double log normal distribution

I apologise if this is a duplicate, i couldn't find a thread that seem to be talking about the same thing. I have a dataset with a bunch of duration of varying lengths in seconds, i log-transformed ...
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### Sum of two exponential series with equal means and variances

Assuming $A$ and $B$ are two non-negative real-valued random variables such that $\mathrm{E}(A)=\mathrm{E}(B)$ (equal means) $\mathrm{Var}(A)=\mathrm{Var}(B)<\epsilon$ (equal small variances) is ...
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### Is MLE of $\theta$ asymptotically normal when $(X,Y)\sim e^{-(x/\theta+\theta y)}\mathbf1_{x,y>0}$?

Suppose $(X,Y)$ has the pdf $$f_{\theta}(x,y)=e^{-(x/\theta+\theta y)}\mathbf1_{x>0,y>0}\quad,\,\theta>0$$ Density of the sample $(\mathbf X,\mathbf Y)=(X_i,Y_i)_{1\le i\le n}$ drawn from ...
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### Designing hypothesis test around failure rates

I'm trying to devise a hypothesis test for failure rate data of machines. The gist is that there are some machines in a factory that run all the time. They fail from time to time and are promptly ...
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### How can I make a Kolmogorov-Smirnov test to check if my data distribution is exponential?

I made a histogram of my data, and the fitting line, but from some reason the fitting line doesn't fit to my graph. How can I make it fit to it? How can I check if my data distribution is exponential?...
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### If $X$ is from (canonical) exponential family, do we always know the distribution of $T(X)$?

Assume $X$ are generated by a distribution from exponential family, $$f(X; \theta) = h(X)\exp\{\eta(\theta)T(X) - b(\theta)\}$$ After solving several exercises with various distribution functions, ...
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### Manually calculating the survival probability S(t) from flexsurv exponential regression parameters in R

I am learning survival analysis for my research. My question is very basic. I created a simulated dataset as shown below: ...
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### How to properly truncate exponential distribution to represent random memory-less arrivals?

Typically, Poisson and exponential distributions are used to represent random memory-less arrival processes. It has come to my attention, however, that a more realistic distribution is a truncated (or ...
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### Exponential Distribution - Memoryless and examples

In several (introductory) statistics books we can see that they use an Exponential Distriubtion to model the time of failure of an electronic component. I understand that it got the appealing property ...
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### Why is sample mean minus location parameter of shifted exponential gamma distributed?

My book says the following Suppose $X_{i} \sim$ iid $Exp(1,\eta)$ Where $Exp(\theta,\eta)$ is the shifted exponential ie has density $$\frac{1}{\theta}e^\frac{-(x-\eta)}{\theta}$$ for $x \ge \eta$ ...
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### median survival derived from a mixture of exponential distributions

I recently got a very nice question... Let's say that we have one cohort, and we know the median survival of it. Then we split the cohort into two groups, and somehow we also know the median survival ...
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### Transforming back after a log transformation with subtraction

I needed help with back transforming my data. My initial data was positively skewed so I had to log transform it, after which I did my statistical test. One of my regression test required for my ...
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### 95% Confidence interval of $\lambda$ for $X_1,…,X_n$ IID exponential with rate $\lambda$

I know how how to find the estimation of $\hat{\lambda}$ using the method of moments. I can take the first moment and equate it to the empirical to get, \$E(X) = \frac{1}{\lambda} = \frac{\sum_{i=1}^{...
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### Exponential Test

Given a collection of data points, without any other information I want to test for an exponential distribution. In a different case, I tested for normality using an Accord implementation of the ...
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### Alternative heavy right tailed distribution to exponential distribution

I have data whose distribution resembles an exponential distribution, but the data has a heavier tail than the exponential distribution. I will be very glad for any recommendation of an alternative ...
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### calculate quantile for exponential distribution

My distribution function is: y=a * exp(-b*x) What is the right way to calculate first Quartile? Right now I do like that: Q1=ln(4/3)/b Is that correct?