Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [exponential]

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

0
votes
0answers
6 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 ...
1
vote
1answer
36 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 ...
0
votes
1answer
43 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?
0
votes
0answers
9 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 ...
0
votes
0answers
27 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}{\...
0
votes
1answer
43 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, ...
3
votes
0answers
38 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 ...
0
votes
0answers
78 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 $\lambda_y$ ...
2
votes
1answer
64 views

Finding variance of infimum of a set

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{...
3
votes
2answers
54 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 ...
2
votes
1answer
63 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 $c_{\alpha}, d_{\alpha}$ ...
1
vote
1answer
45 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 ...
0
votes
0answers
16 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 ...
0
votes
1answer
28 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 ...
2
votes
2answers
38 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=\...
-3
votes
1answer
64 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),...
1
vote
1answer
71 views

Confidence interval for $\sigma^2$

I started with any distribution and underwent the CLT on $\sqrt{n}(\widehat{\sigma}^2 - \sigma^2)$ where $$ \widehat{\sigma}^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2 $$ is a sample mean of $\sigma^2$...
1
vote
0answers
45 views

Exponential Family Representation: Dumb question on scale parameter and whether it went to Hawaii

So going over the Hastie Tibshirani paper on GAM - it points to equation 11 as the exponential family density - but with two parameters - theta (natural parameter) and phi (scale). https://...
0
votes
0answers
12 views

Find joint distribution for two different cases Kruskal Wallis

I'm a bit stuck with my homework in a subject called "Non-parametric Statistics". The task is related to Kruskal-Wallis test. The task is as follows: Let's look at the comparison of 3 independent ...
2
votes
1answer
43 views

The probability distribution of waiting time until two exponentially distributed events with different parameters both occur

I am working on a problem related to the waiting time until a parking garage is empty. We are given that the cars independently spend an exponential distributed time in the parking garage, with ...
5
votes
1answer
127 views

What should my critical region look like in this LR test for shifted exponential distribution with pdf $e^{-(x-\theta)}\mathbf1_{x>\theta}$?

I have a small confusion over describing the cutoff point for the critical region in a likelihood ratio test when the null hypothesis is composite. Take this exercise in particular: Let $(X_1,X_2,\...
2
votes
1answer
44 views

probability that matrix $2\times2$ of Random variables is Invertible

Let $X_1, X_2, X_3, X_4$ to be Variables, and let $A$ be the following matrix: $$ \left[\begin{matrix} X_1 & X_2\\ X_3 & X_4 \end{matrix}\right] $$ assume that $X_1, X_2, X_3, X_4$ are ...
1
vote
0answers
55 views

Exponential heteroskedasticity

Assume that the form of heteroskedasticity is exponential such that $u_{i} = e^{0.5X_{i}\gamma}\upsilon_{i}$ where it is assumed that $\upsilon_{i} \mid X_{i} \sim N\left(0,1\right)$ and $X_{i}$ ...
0
votes
1answer
51 views

Differences between exponential distribution with very different n sizes

I need to test for the differences between three groups of observations (grouped along $x$-axis), which appear to follow an exponential distribution along the $y$-axis dimension (see example fig.). ...
0
votes
0answers
34 views

Does exponential waiting time for an event imply that the event is Poisson-process?

Say I have a process, $\{N_t : t \ge 0\}$, which denotes the number of the event that occurred until the time $t$. And let me define $W = \min \{t : N_t = 1\}$ which is denotes the time until the ...
4
votes
1answer
58 views

Marginal Distribution of Exponential Mixture Model

I am currently trying to marginalize over the scale parameter in a mixture distribution of exponential pdfs, but I do not trust my result. Let me show you my steps: Probability Density Function The ...
0
votes
1answer
98 views

Survival time problem exponential with gamma prior

The survival times, in days, of patients diagnosed with a severe form of a terminal illness are thought to be well modelled by an exponential($\theta$) distribution. We observe the survival times ...
1
vote
0answers
19 views

Using fitted lagged variable as dependent variable in a new regression?

Suppose I have regression like this; $y[t] = a * exp(b*y[t-1])$ From this regression, I get; $\bar y = y - residuals$ What happens if I regress a new regression like this? $y[t] = c * exp(d*ybar[t-...
2
votes
1answer
127 views

Memoryless property of exponential

Let $X$ be an exponential random variable. I have been asked to evaluate whether each of the following is true or false and am seeking some insight about a solution that was offered. $(a) E(X^2 |X>...
0
votes
0answers
8 views

Test if long-term growth rates are constant

For example, consider U.S. economic GDP. This appears to be growing exponentially over time. Clearly, annual GDP growth is sometimes high and sometimes low. But say that one person claims that, over ...
0
votes
0answers
17 views

First moments of GBM-like process with non-normal shocks

First consider a standard GBM process of the form, $$\frac{dS_t}{S_t} = \mu dt+ \sigma dW_t$$ but instead of the normal $W_t \sim N(0,1)$ , instead we have that $W_t \sim EMG^-(0,1,\lambda)$. Where ...
1
vote
2answers
55 views

Finding pdf with more than one random variable

I am stuck with a question doing one of my stats tutorial and question is as follows: Suppose X and Y are two independent exponential random variables with parameter $\theta$, i.e. their joint ...
3
votes
0answers
45 views

What is the limit of this expression?

If $\det(\Lambda_0) \to 0$, what does $$ \exp\left(-\frac{1}{2}\text{trace}\left(\Lambda_0 \Sigma^{-1}\right)\right)\det\left(\Lambda_0\right)^{-1/2} $$ approach? I was trying to answer the ...
1
vote
0answers
54 views

Hypothesis test for machine failure rates

Let's say I have one collection of machines (made by manufacturer 1). These machines run over a few days and fail at a certain rate. Let's say they run for a total of $h_1$ machine hours and the ...
0
votes
0answers
28 views

Probability of stale cache hits w/ exponentially distributed read and write inter-arrival times

I am trying a create a model for a very simple system which consists of a server and 2 clients: R and W. The server stores a piece of data D and hands out leases for caching D on the clients. The ...
0
votes
1answer
221 views

Discrete Fourier transform of an exponential decay

I have a vector with an exponential decay signal, using Numpy: t=np.arange(128) a=0.1 decay=np.exp(-a*t) I would like to compute the discrete Fourier transform (...
0
votes
1answer
38 views

What probability distribution can be described as y ~ X * Exp(1) [closed]

The green dots show the product of X and the exponential distribution with rate 1. It looks like it should be some simple probability distribution but I can't figure out what it is! Can you tell me ...
0
votes
2answers
121 views

Batch loss of objective function contains exp becomes nan

I am trying to solve a survival analysis problem, where all data are either left-censoring or right-censoring. I use an objective function which contains the CDF of Gumbel distribution. I have $m$ ...
0
votes
0answers
35 views

exponential of Covariance of two variables in logs, cov(X,Y)=exp(X)*exp(Y)*cov[ln(X),ln(Y)] [duplicate]

I am stuck in calculating steady state in a model that has covariances in logs. I am wondering in general if the following accurate. cov(X,Y)=exp(X)*exp(Y)*cov[ln(X),ln(Y)] if that is accurate ...
3
votes
0answers
110 views

Is the truncated power law a heavy-tailed distribution?

A heavy-tailed distribution is often defined as a distribution with a tail that is not exponentially bounded. A truncated power law (or power law with exponential cut-off) is a distribution that ...
1
vote
1answer
41 views

Censored regression methods for analyzing extreme end of a normally-distributed variable

I have a normally distributed continuous variable referring to an observed human behavior, and I'm interested in measuring or rather analyzing the extreme of this behavior, namely, the top 10% of the ...
1
vote
0answers
375 views

Prove that the interarrival times of a Poisson Process are all indipendent and identically distributed

{$N_t$} with $t\in \mathbb{R}$ is a Poisson process with intensity $\lambda \in \mathbb{R^+}$, so that 1) $N(0)=0$, 2) {N(t) is with indipendent increments and omogeneous increments and 3) $\...
0
votes
1answer
47 views

Prior for mean unknown parameter

We know that there are two versions of exponential $\big(1\big)$ $exp(\lambda)$ with pdf $$f(x;\lambda)=\lambda e^{-\lambda x}$$ ,$\lambda>0,x>0$ and $\mathbb{E}[x]=\frac{1}{\lambda}$ for ...
0
votes
0answers
17 views

How to model exponential decay with seasonality

I am trying to model sales driven by marketing tactics with promotional deadlines in Excel. The overall trend of the sales driven by each marketing tactic decays exponentially following the launch ...
2
votes
1answer
103 views

Interpretting the p-value when inverting the null hypothesis

I'm performing an analysis by fitting data points to an exponential distribution and testing the adequacy of this fit using the Kolmogorov-Smirnov test. The standard ks test null hypothesis: the data ...
1
vote
1answer
131 views

How to calculate mortality rate or probability of death at time t for various parametric distributions, e.g. Weibull, exponential, log-normal

If I have lambda and gamma, can I estimate that the probability of death at time t, based on a Weibull distribution is: What are similar formulas for the exponential, Gompertz, log-normal, log-...
2
votes
1answer
137 views

Piecewise exponential model - how to fit

I'm trying to go through the following paper: https://projecteuclid.org/download/pdf_1/euclid.aos/1176345693 it covers the piece wise exponential model for modelling hazard rates in a non-parametric ...
1
vote
1answer
345 views

Exponential Smoothing & Seasonality

I am relatively new to stats and forecasting and was hoping to tap the wisdom of this community in regards to a question. One of my colleagues insists that exponential smoothing presumes seasonality. ...
0
votes
1answer
77 views

Normalize number according to exponential function

I haven't picked up a math book in a while so please be patient. I have a series of numbers ranging from zero to infinity (realistically up to 10 though) and I want to normalize these values to 1 to ...
0
votes
1answer
95 views

Linear regression and exponential distribution

I'm running a simple ordinal least squares regression. My dependent variable is normally distributed, while my independent is exponentially distributed. Will this be a problem and, if yes, is there a ...