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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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25 views

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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31 views

is this sampling from a simplex?

Simply, if I sample $n$ $X_i$s from an exponential distirbution; that is $$ X_i \sim exp(1) $$ Then prove that the vector $$ \left ( \frac{X_1}{\sum X_i}, \frac{X_2}{\sum X_i}, \cdots, \frac{X_n}{\...
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14 views

Mix pdf and cdf in binary response model [duplicate]

Let's suppose that I have a model that tells me how likely is for an event to have come after a certain time lapsed, given by some kind an exponential distribution, i.e. $$ \mathbb{P}(T_E < t) = \...
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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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9 views

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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49 views

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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41 views

Sum of exponentials and variance of the exponents

Let's assume we have two sets of non-negative real-valued numbers $\{a_i\}_{i=1}^{N}$ and $\{b_i\}_{i=1}^{N}$ ($N$ can be large) such that $\frac{1}{N}\sum_{i=1}^{N}a_i=\frac{1}{N}\sum_{i=1}^{N}b_i=...
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53 views

P-value of an exponential model

I am a statistics noob, so bear with me. I have an predictor variable BMU and a response variable T. I hypothesize the two ...
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59 views

Convolution of a multivariate Gaussian and multivariate exponential distribution

I have derived the convolution for a multivariate Gaussian distribution with a multivariate exponential distribution. The aim is to get a multivariate extension to the univariate exponentially-...
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1answer
50 views

Expected value of $e^{vS}$, where $S$ is an exponential

I am studying queueing theory and in particular I am dealing with priority queues with preemption. I found this very interesting paper that treats various topics of interest. The system is composed ...
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50 views

Determining under what conditions an exponential function is linear

I'm working through an exercise to determine when an exponential function of the form: y = ae^(bx)+c is approximately or exactly linear (of the form ...
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3 views

Sampling method to represent a larger demographic

I have a set of Google search queries for a particular user. Every query has its frequency, that is the number of times the person searched it for. Now I have to infer some information about this ...
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1answer
79 views

Identifying a distribution

I am trying to understand what sort of distribution is produced by the following code. Using the following Matlab code we can generate a distribution (normalized such that the sum of the set is equal ...
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1answer
107 views

Does the sum of two independent exponentially distributed random variables with different rate parameters follow a gamma distribution?

short question. Suppose we have two independent exponentially distributed random variables with means $400$ and $200$, so that their respective rate parameters are $1/400$ and $1/200$. Do these ...
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31 views

Maximum entropy probability distribution over non-negative support and finite mean?

I'm trying to derive which univariate probability distribution maximizes entropy, assuming finite mean $\mu$ and non-negative support $[0, \infty)$. I know that the answer is the exponential ...
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19 views

Why knowing information about something doesn't help when it comes to Exponential Distribution?

I've recently learned about Exponential Distribution and when it's appropriate to be used. There was the following example given. The duration of IC555 integrated circuits under normal operation ...
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1answer
173 views

Two-sided UMP test for exponential densities?

I'm struggling with a problem from Lehmann & Romano's book *Testing Statistical Hypothesis." Suppose $X_i$ is a random sample from $$f(x) = \frac{1}{b}e^{-(x-a)/b}\mathbf{1}_{x>a}$$ The ...
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34 views

Binomial distribution in exponential form

I am trying to find out if I am doing this right: I have started with: $f(y)=\binom{n}{y}(\frac{\mu}{n})^y(1-\frac{\mu}{n})^{n-y}$ This is what I get: Result: $exp[ylog(\frac{\mu}{n-\mu}) - nlog(1+e^...
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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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1answer
23 views

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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49 views

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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333 views

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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190 views

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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1answer
45 views

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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1answer
41 views

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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35 views

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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21 views

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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21 views

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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2answers
42 views

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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1answer
25 views

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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60 views

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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2answers
509 views

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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15 views

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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1answer
39 views

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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1answer
282 views

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?
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19 views

How to model count data with decay

I'm trying to understand how I might model count data where there's diminishing marginal utility and a stochastic process. So, let's say we're modeling the number of "useful intelligence tips" given ...
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147 views

Bus arrival times and exponential distribution

I came across a question that is supposed to show us how the properties of the exponential distribution can be used. I know and have shown that $$P(X_i<min\{ X_1,\dots,X_n\})=\dfrac{\lambda_i}{\...
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1answer
314 views

how to draw 100 numbers following exponential distribution (erlang) in python by having k and CV and mean exponential distribution?

how to draw erlang distribution (two parameters k and cv? (k=1,5,10, cv=100%-45%-32%) ) in python by having k and CV and mean exponential distribution=1? I know numpy.random.exponential(scale=1.0, ...
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50 views

two independent Poisson Arrivals

I have two types of customers (type 1 and type 2) enter a shop. Their arrival processes are independent and follow Poisson process with the arrival rates of $\lambda_1$ and $\lambda_2.$ Consider two ...
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127 views

Conditional expectation of an exponential variable

I have trouble with conditional probabilities, therefore I am wondering if the following derivation is correct: Both X and Y are exponential random variables, with $\lambda_x$ and $\lambda_y$ ...
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1answer
89 views

Finding variance of infimum of a set [duplicate]

Let $X_1, X_2, \cdots,X_n$ be independent and identically distributed random variables having an exponential distribution with mean $\frac{1}{\lambda}$. Let $S_n=X_1+X_2+\cdots+X_n$ and $N = \text{...
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2answers
102 views

Best regression model for data that shows exponential decay, but has and is bounded by zero

Fairly new to regression analyses. I have a data set for a clinical metric that is bounded in the range of [0-38] for a number of anonymized patients. I want to develop a regression model that ...
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1answer
183 views

UMAU confidence interval for $\theta$ in a shifted exponential distribution

Suppose $X_1,X_2,\ldots,X_n$ is a random sample drawn from the distribution $$f_{\theta}(x)=e^{-(x-\theta)}\mathbf1_{x>\theta}$$ It can be shown that there exist some $c_{\alpha}, d_{\alpha}$ ...
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1answer
114 views

What does it mean by “approach the performance of the Bayesian gold standard”?

It is a sentence in Dropout paper(Dropout: A Simple Way to Prevent Neural Networks from Overfitting). "This can sometimes be approximated quite well for simple or small models, but we would like to ...
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27 views

Class frequency comparison (exponential distribution)

I have two different sources of data and I would like to check if their class distributions are similar and how much. The first dataset ($D_1$) has 2M samples and the second ($D_2$) 6M. When I ...
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1answer
50 views

Can I use the exponential distribution to model data with some negative values?

my data ranges between x=(-10, 60). X represents energy savings after adopting an energy efficient product, where most individuals save energy (positive x) but a few use more energy (such as through ...
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2answers
63 views

Linearization of multiplicative and exponential regression models and their OLS estimation

So far I have been under the impression that you can "linearize" multiplicative models of the form (1) $y=\alpha * \beta_1x_1 * \beta_2x_2 * \beta_3x_3 $ and exponential models of the form (2) $y=\...
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94 views

Distribution of a function of exponential and uniform random variables? [closed]

Consider the following independent random variables: $$\begin{equation} \begin{aligned} A &\sim \text{Exp}(\lambda_1), \\[6pt] C &\sim \text{Exp}(\lambda_2), \\[6pt] B &\sim \text{U}(0,1),...