Questions tagged [logistic-distribution]

A symmetric distribution which CDF is the logistic function.

Filter by
Sorted by
Tagged with
2
votes
2answers
27 views

Regression with Logistic-Distribution errors (NOT Logistic Regression)

I was wondering if anyone ever tried to do a regression where the errors, instead of normal, would be assumed to be from the Logistic Distribution. I don't mean Logistic Regression, as I don't assume ...
0
votes
0answers
38 views

Bias-variance decomposition for logistic distribution

Probably a stupid question. The expected test mean squared error for a machine learning regression model can be written as: $E\left[\left(y_{0}-\hat{f}\left(x_{0}\right)\right)^{2} \mid X=x_{0}\right]=...
0
votes
1answer
56 views

Method of moments and MLE

Suppose a random variable follows the logistic distribution, $X ∼ Logistic (\mu, \sigma)$ and we restrict our attention to random samples drawn from this random variable $X$. What would be the MoM and ...
0
votes
1answer
39 views

When should you not use logistic regression GLM with a binary response variable?

I came across a set of data that does not seem to "flip" from 0 to 1 (binary response variable) when the predictor variable increase. Thus, this is the plot I got after plotting the ...
4
votes
1answer
90 views

What is $\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$ for $c\in\mathbb{R}$

It is straightforward to show $$\int_{-\infty}^{\infty}\Phi(a+bx) \phi( x ) dx = \Phi\left(\frac{a}{\sqrt{1+b^2}}\right)$$ but what value does $$\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$$ have for $c&...
0
votes
1answer
39 views

Relation between logistic regression and logistic distribution [duplicate]

When we are using logistic regression, we can get the probability that $y$ belongs to class $1$ as follows: $P(y=1|x;\theta)=\frac{1}{1+\exp(-\theta^Tx)}$. PDF of a logistic distribution is given as ...
2
votes
1answer
56 views

A Gaussian scale mixture representation of the logistic distribution

Can the logistic distribution with density function $$f(x) = \frac{e^{-x}}{\left(1 + e^{-x}\right)^2}$$ be represented as a Gaussian scale mixture? In other words, if \begin{align*} X|V &\sim N(0, ...
0
votes
1answer
24 views

What is (are) scenerios and practical settings that can possibly lead to the weibull-log-Logistic mixture distribution?

In my paper I studied Weibull-loglogistic mixture distributions in reliability and life testing, some structural properties of the model are presented including moments, reliability, hazard rate ...
1
vote
0answers
29 views

What are assumptions for logistic binomial regression if all independent and independent variables are dichotomous?

I have three independent and one dependent variables of the dichotomous type and I am trying to use logistic binomial regression. I have 117 observations in total. When I read the literature, some of ...
0
votes
1answer
29 views

logistic distribution

Is it true that almost every discrete data set containing positive values follow logistic distribution if the data set is log-transformed and standardised(subtracting mean and dividing by standard ...
0
votes
0answers
8 views

What logistic function 's mean have to do with vanishing gradient? [duplicate]

In case of logistic activation function Going forward in the network, the variance keeps increasing after each layer until the activation function saturates (slope becomes 0) at the top layers. This ...
1
vote
1answer
245 views

What form of conjugate prior best fits this likelihood distribution? [closed]

Joint likelihood of a two part model consisting of logistic regression and log-normal model:
1
vote
1answer
27 views

Change of variable for logistic distribution to loglogistic - where do I go wrong?

Similar to what I described in this post I would like to make the following change of variable $$Y := \exp( \eta + \sigma e ), \sigma>0 $$ where $e$ has the standard logistic density $f_E(e) = \exp(...
3
votes
1answer
233 views

Comparison of logit and probit estimations

There are a lot of questions concerning logit and probit relations (led by 20523), but I'm still confused with a seemingly simple issue. On the one hand, often we see that for 'rule-of-thumb' ...
1
vote
1answer
91 views

How to invert a mixture of log-logistic distributions? [duplicate]

Say I have a CDF of the form $$F(x) = \sum_{i=1}^n \frac{ k_i }{ 1 + (x/\alpha_i)^{ - \beta_i } }$$ $$\sum_{i=1}^n k_i = 1$$ How do I find the quantile function, i.e. how do I invert F for n>1? I ...
0
votes
1answer
28 views

How to specify a risk model?

I'm reading this article. The authors indicated that for a random sample of 12 characteristics and 3600 patients affected in two arms (control and treatment arm), they fitted a risk model consisting ...
4
votes
2answers
382 views

What is the probability distribution used in logistic regression called?

In logistic regression, we set the probability of predicting a target $y$ given a data $x$ as, $\Pr(Y = 1|X;w) = \dfrac{\exp(w^TX)}{(1+\exp(w^TX))}$ What is exactly this probability distribution (or ...
0
votes
1answer
52 views

Independent variables should have exponential distribution in logistic regression

As per my understanding of logistic regression, a log of odds of the desired value of “y” should be in linear relation with the log (x). Does that mean that independent variables should have ...
0
votes
0answers
56 views

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 ...
2
votes
1answer
93 views

How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ for the logistic distribution?

Take the cumulative distribution function (cdf) $\Phi(z) = \frac{1}{1+\exp(-z)}$ and probability density function (pdf) $\phi(z)=\Phi(z)(1-\Phi(z))$ of the logistic distribution. How can one calculate ...
1
vote
0answers
39 views

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 ...
4
votes
2answers
872 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 \...
0
votes
0answers
38 views

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)}{(\...
2
votes
2answers
101 views

Is there a connection between the normal and the logistic distribution?

Regarding Bayesian statistics I found in a script that there is such link, and the logistic arises in context of a normal distribution and a "binary state". However, I have no idea what is the meaning ...
1
vote
1answer
76 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 ...
4
votes
3answers
4k views

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 ...
1
vote
2answers
285 views

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 ...
0
votes
1answer
284 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 $(\beta_1, \beta_2)$...
0
votes
1answer
2k views

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 ...
0
votes
1answer
268 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 ...
2
votes
1answer
993 views

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-...
1
vote
0answers
76 views

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 (...
1
vote
2answers
207 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 ...
23
votes
3answers
3k views

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?
1
vote
0answers
190 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 ...
2
votes
1answer
527 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 ...
46
votes
4answers
38k views

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 ...
2
votes
1answer
217 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 ...
2
votes
3answers
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 ...
2
votes
1answer
239 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 ...
2
votes
1answer
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 ...