Questions tagged [logistic-distribution]

A distribution which CDF is the logistic function.

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Location and scale estimation for log-logistic in scipy

I have to estimate the location and scale parameters for a log-logistic or fisk distribution using scipy. The shape parameter is already defined and I would like to estimate loc and scale parameter ...
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“Hazard function” for logistic PDF

Question: Does hazard function $h(x, \mu, \sigma)=\frac{f(x, \mu, \sigma)}{1-F(x, \mu, \sigma)}$ of logistic PDF $f(x,\mu, \sigma)$ make sense? The problem is that logistic PDF is defined for ...
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How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ for the logistic distribution?

Take the distribution function $\Phi(z) = \frac{1}{1+\exp(-z)}$ and density function $\phi(z)=\Phi(z)(1-\Phi(z))$ of the logistic distribution. How can one calculate the integral below? $$\...
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Logistic Regression For Classification [duplicate]

The origin of logistic regression is actually logistic curve which varies from the value 0 to the value 1. It looks like the letter S, and it specifies the growth of species. If our data distribution ...
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Logistic regression - binary to continuous - how to interpret?

Given data with a binary outcome, i.e.: $0$ = no event, $1$ = event which can be modeled with logistic regression, how then do we understand the following logic: ...
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135 views

How is Logistic Regression related to Logistic Distribution?

We all know that logistic regression is used to calculate probabilities through the logistic function. For a dependent categorical random variable $y$ and a set of $n$ predictors $\textbf{X} = [X_1 \...
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Generalized logistic distribution

I saw on wikipedia https://en.wikipedia.org/wiki/Generalized_logistic_distribution that when $\alpha<\beta$, generalized type IV logistic distribution can be written as: $\frac{\exp(-\alpha x)}{(\...
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Approximation or closed form equation for summation of logistic function [closed]

The spread of epidemics follows a logistic growth, given in the equation below $I(t) = \frac{N}{1+(N-1)exp^{-rNt}}$ where, N is the population size, r is infection rate, t is time , I(t) is ...
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46 views

Infinite continuous response variable for logistic distribution? GLMM

When I would like to use the generalized linear mixed model (GLMM) for my data analysis, I would have to check the distribution of the response variable so as to decide the link-function. The result ...
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How to visualise coefficients of a Binomial Logistic Regression?

Hello all! Do you have an idea how best visualise the data from this table knowing they are coefficients of binomial logistic regressions? What I would like to visualise is a confrontation between ...
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Logistic Regression Models Without Main Effects?

I am building logistic regression models measuring human behaviour, which consist of categorical variables: demographics, conditions, and interactions between the demographics and the condition ...
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Plotting the results of a logistic regression

I ran a logistic regression in R and then I went to plot it and I'm not sure how to understand the plot. Here's the logistic regression - ...
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140 views

Getting logistic distribution from student's t-distribution

How can I get the probability density function (PDF) of standard logistic distribution from the PDF of symmetric student's t-distribution with location and scale parameters. In the $(\beta_1, \beta_2)$...
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Use of KS statistics to choose the probability cut-off in logistic regression model [closed]

I was doing some reading on choosing the score cut-off of a logistic regression model using the KS-Stats. Suppose I fitted a logistic regression model on the train data and now want to decide the ...
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227 views

interpretation of logistic coefficient

I have some toy data for an experiment where subjects are shown pictures A,B and C and then they are given a choice between choice A or choice B. I am interested in determining the effect of the ...
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does logistic distribution belongs to exponential family

Let $X$ have the logistic distribution with the PDF $$f(x) = \frac{\exp(-x-θ)}{(1+\exp(-x-θ))^{2}}$$ Does $f(x)$ belong to the exponential family? My solution is $\exp[(-2)\cdot \ln(1+\exp\{-x-θ\})-x-...
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Calculate sample mean confidence interval of noisy logistical distribution

I have $n$ samples which follow a logistic distribution with unknown $u$ and $s$; it is affected by a Gaussian noise with 0 mean. I would like to estimate its average $u$ with a confidence interval (...
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148 views

t-test with logistic and Gumbel distributions

I know that one of the basic assumptions of a t-test is that the data is drawn from a Gaussian distribution. Using an Anderson-Darling test, I've found that the datasets I am working with are either ...
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Why is the logistic distribution called “logistic”?

What is "logistic" about the logistic distribution, in a common sense way? What is the etymology of and the lexical rationale for the name, not just pure math definition?
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157 views

Find an unbiased estimator from a random sample from the logistic distribution

So I'm not sure where to start on this one, so any hints will help me because I'm a little lost on finding unbiased estimators. So suppose $X_1, X_2,... X_n$ is a random sample from the logistic ...
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408 views

Obtaining the Log-logistic distribution from a truncated logistic distribution

Let $$f(x) = \frac{e^x}{(1+e^x)^2}~,~ -\infty \lt x \lt \infty~~~~~(1)$$ be the standard logistic pdf of a random variable $X$. Then one can obtain the pdf of the log-logistic distribution via the ...
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Logistic Regression - Error Term and its Distribution

On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in ...
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1answer
195 views

How to compute for Bivariate Logistic Distribution

This is the logistic distribution of single random variable (taken from Wikipedia). $x$ = random variable $\mu$ = mean of all random variables $s$ = variance. Now, I want to do a Bivariate logistic ...
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2k views

Multivariate logistic distribution

The normal distribution can be generalized into the multivariate normal distribution. Can the logistic distribution also be generalized into a similar multivariate distribution? Is there a ...
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1answer
214 views

What is this distribution? Inverted S / cursive N

I have come across a graph pattern in two basically unrelated experiments, and I want to understand where it is coming from, or at least how to handle it statistically. I work in computational ...
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2k views

Test for a logistic distribution in R

I have a set of data and I'd like to know whether this data set has a logistic distribution. When I made a histogram of my data set it seems to have a logistic distribution, but to be sure I'd like to ...