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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Confidence intervals cross exponential regression when predictors scaled across zero but not when positive

I'm running non-linear regression analyses in R using the nls() function, and I've noticed some strange behavior with a particular analysis. If the independent variables contain both positive and ...
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R: Fit regression to asymptotic data

I'm trying to fit a regression to data with a decreasing exponential shape, i.e.: I have two data sets which I know should conform to this shape, shown in blue and green below: So, I'd like to fit a ...
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What is the objective function to optimize in glm with gaussian and poisson family?

I am reading this post and still confused about the different ways of fitting exponential data. Specifically, why I am getting different results with following code? Could anyone help me to write down ...
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Inferring an approximate distribution for noising of data given 300,000 samples of human noising [closed]

I'm trying to find a statistical way to get an approximate distribution of all human noising. I have a dataset of over 300,000 samples of people noising words. I took basic Statistics and I would know ...
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Likelihood Ratio test of exponential distribution with H0 u1=u2=u3 [closed]

Suppose that three independent random samples of sizen1,n2andn3observationsare obtained. LetX1,...,Xn1andY1,...,Yn2andZ1,...,Zn3be the three randomsamples, with sample meansXandYandZ, ...
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Realization of a Beta distribution function from a derived Exponential function

So we have a beta distribution Y∼Beta(1,β) and a random variable X which is given by the equation X=−log(Y) I found the cumulative distribution function of Y to be Then I found the cdf of X So X is ...
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What are the similarity and difference between fitting exponential distribution and exponential growth / decay?

A classic example of exponential growth is the population at early stage, and exponential decay will be some radioactive decay. From my understanding, they are deterministic and no randomness in there....
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Can we infer other distributions from the distribution of the 99th percentile?

This is a fairly weird question, but I'm analysing a paper that reports its findings in a curious way; for every subject, they passively took measurements every 10 seconds for 24 hours (8640 ...
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Fit exponential growth: should I fit the cumulative or incidents per day?

Suppose we want to fit an exponential growth model on some disease outbreak, should we use the cumulative count or incidents per day count? According to my understanding we should use the cumulative ...
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Exponential Decay Model (Variable) in R

I'm working with a large time-series data set where I am trying to estimate the decay rate over a period of 66 months. The variables of importance to my question include: ID = Personal ID #, Date= the ...
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Exponential Reestimation Formula in EM Algorithm

I'm trying to understand how to reestimate parameters, as part of the EM algorithm. As a simple example, I'm trying to derive the reestimation formula for an exponential distribution. Here's the setup:...
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If number of infected people grow exponentially, is R0(basic reproduction number) the coefficient in exponential function?

I am trying to learn basic reproduction number and have a very basic question. In a given time window, If number of infected people grows exponentially, for example $N_{d+1}=1.15N_{d}$ Can we say ...
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Survey of Deep Learning Linear Combinatorial Optimization

I have the task of developing an AI based combinatorial optimization algorithm involving a complex mix between TSP and Knapsack: A path must be found connecting millions of nodes and the cost ...
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Exponential distribution memoryless question [closed]

Can someone explain why E[Y] = 0.9 would imply the probability in the solution?
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Effectiveness test of intervention on number of cases

Apologies if I'm phrasing this incorrectly, I want to model the effectiveness of an intervention measure on the number of patients diagnosed with a virus (COVID-19). A hypothesis test of sorts comes ...
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Large Set of Random Variables with Exponential Distribution

I'm struggling to understand how to solve the following problem. I have a random variable $X$ that represents the life time of a cellphone (in years) and I know that such variable follows an ...
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Interpreting and troubleshooting nls in R with quadratic plateau model

I am trying to run a quadratic plateau model on some proportion data where values are bound between 0 and 100. I would like some help troubleshooting some errors I have encountered, and correctly ...
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Non-monotone Survival Function?

I was given the task of plotting the graph of a survival function with the following details defined. hazardrate (lambda) = λ(t) = 0.2 (1 + sin(tπ/12)) the underlying process is exponential I am ...
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Compare two Kolomogorov tests with exponential distribution

I try understanding implementation of Kolomogorov test for one Sample. ...
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Sum of exponential of uniform random variables?

Let $F_{i}$ and $\phi_{i}$ are uniformly distributed independent random variables in the range $[-50,50]$ and $[-\pi/4,\pi/4]$, respectively. If $N = 10$ and $$Z = \sum_{i=0}^N e^{j(F_{i}+\phi_{i})}...
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What is the probability that X=Y<Z

Let $f(x,y,z)=e^{-x-y-z},\,x>0,y>0,z>0$ and 0 elsewhere, be the joint PDF of (X,Y,Z). Compute, $P(X=Y<Z).$ I started the answer as follows. $\begin{align*} P(X=Y<Z)=\int_{z=0}^\infty\...
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Why is e^-alpha

I'm an Education major taking computational statistics. I'm having trouble figuring out how a variable (alpha) distributed as an exponential (lambda = 1) can be expressed as e^-alpha. We're covering ...
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Prove that argmin of exponential distributions has multinomial distribution [closed]

Let's say we have $ T_1,T_2,\cdots,T_n \sim Exp$ and $P(X_1>a)=e^{-\lambda_1 a},P(X_2>a)=e^{-\lambda_2 a},\cdots,P(X_n>a)=e^{-\lambda_n a} $. How can I describe $\DeclareMathOperator*...
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Differences between approaches to exponential regression

One could fit an exponential in many different ways. This post suggests doing the down-and-dirty lm on the log of the response variable. This SO post suggests using ...
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Erlangian deterioration process with alternating lambda (each a probability)

I have an erlangian deterioration process with 10 deterioration states, including initial (state 1) and failed (state 10) states. The lambda (yearly rate) alternates between three values, 0.5, 7.0 and ...
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How to combine/pool the standard error of fitting parameters from multiple fits of the same model?

Let me first explain the context of the problem: I have a time series of the (z-)positions of a particle relative to a surface. For 5 independent subsamples of this time series, I calculate the ...
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Is the ratio of two noncentral exponential distribution the logistic distribution?

Is the ratio of two noncentral exponential distribution the logistic distribution? If yes, How to set the parameter of the logistic distribution using the parameters of noncentral exponential ...
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Sampling distribution of exponential sample variance (formal not empirical)

Addressing this problem: Let $X_1, ..., X_n$ be iid exp($\theta$) with pdf, $f(x)=\frac{1}{\theta}e^{-\frac{x}{\theta}}$. What is the distribution of the sample variance? This is to be done by ...
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Sampling Distribution of Exponential Sample Variance (Formal, not Empirical) [duplicate]

Addressing this problem: Let X1,...,Xn be independent identically distributed exponential variables with parameter θ, i.e. with pdf, f(x)=(1/θ)*exp(−x/θ). What is the distribution of the sample ...
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Fitting data to an exponential model with a specified rate in R

I have been using the fitdistr package in R to try and do this but with no luck so far: fit1 <- fitdistr(data1$x, "exponential", start = list(rate = 10)) I am ...
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How to Combine Bernoulli Distribution with Exponential?

I understand a similar question has been asked before but it was closed because the OP left. I have a situation where I have a continuous variable, which can take values between 0.0 -> ~0.1. It ...
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A simple question from my statistics textbook. Exponential distribution (I think) Details in the question

20% of products have to be replaced during the warranty period. How many products must be stored to be able to handle 10 000 orders and the replaces with a probability of 0.9? The book has answers, ...
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Explain the source of overfitting in choosing an additional parameter

I was going through this reddit post. It describes the 'timelapse and prediction of Wuhan coronavirus infections in Mainland China'. The guy chose to use $y=a+b*(exp(c*x)-1)$ to describe the ...
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Multivariate Natural Logarithmic (Exponential) Regression

I have a list of values with 4 input columns and one output column as follows: Temperature: Directly Proportional to Severity Hours of utilization per month: Directly Proportional to Severity Power ...
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How to plot charts symmetrically around 1, like geometrical growth multipliers?

Geometrical growth could be represented as a series of multipliers $V_i = V_0 \prod d_i$. The series will be centred around 1 and when plotted upper side would look larger. When in reality the ...
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Consecutive differences of a uniform law

Let $N>0$ be the number of considered samples. We draw $x_1, \ldots, x_n$ from a uniform distribution over $[0;1]$. We compute $y_1, \ldots, y_{n-1}$ the differences of the sorted $(x_i)_i$. I'd ...
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Want to know the differences between exponential and heavy-tailed distributions in terms of first and third quartiles

What are the differences between exponential and heavy-tailed distributions, please illustrate this difference by explaining how well the first and 3rd quartiles describe them. I know what are ...
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Number of events in a segment if waiting times are drawn from a mixture of two exponential distributions

What is the probability for $n$ events to occur over a period of time $t$, if the duration of each individual event is $\tau_1$ with the probability $p$ and $\tau_2$ with the probability of $(1-p)$? ...
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Distribution of sample maximum from exponential distribution

$x_1,x_2,...,x_n \sim \exp(\mu=1)$ where $x_i$ are independently identically distributed. What is the distribution of $z_n = max(x_1,x_2,...,x_n)-\ln(n)$? Below is my work , I am uncertain whether it ...
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Is a range of values from an exponential distribution still exponentially distributed?

I have to generate numbers of two different exponential distribution ($e_1, e_2$) with parameters respectively $\lambda_1$ and $\lambda_2 = k \lambda_1$, with $0<k<1$. But I also want to ...
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How to fit a distribution with an “10 and more” category at the bottom?

I want to fit a distribution to some data to sample from it in a subsequent simulation. There are I got a dataset that looks somehwat like this: ...
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Estimate the reliability in incomplete data

I have historical data (failure point) for a number of physical servers. These data only consist of the failure observed in 30 days. And, we know the lifespan of the physical server is around 3 to 5 ...
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Bivariate exponential distribution $(S, T)$ with controllable correlation and $S\leq T$

I am trying to define a bivariate exponential distribution $(S, T)$ with marginals $S\sim\mathrm{Exp}(\lambda_S)$ and $T\sim\mathrm{Exp}(\lambda_T)$ for $\lambda_S > \lambda_T$. I would like the ...
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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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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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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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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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