Questions tagged [logistic-distribution]

A distribution which CDF is the logistic function.

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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, ...
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8 views

Item response theory with any cdf link

The IRT applications mostly use as link functions the logit and the probit, which are the cumulative distribution function (cdf) of the logistic and normal distributions, the resulting models gives ...
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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 ...
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17 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 ...
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28 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 ...
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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 ...
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9 views

how do i prove if two independent variables are highly correlated. is logistic variable(true/false) able to perform this test?

In my model all my variable are logistic e.g. have java skill, have python skill can i perform ...
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1answer
80 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:
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1answer
24 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(...
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1answer
121 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' ...
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1answer
66 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 ...
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76 views

Generating function of relaxed Bernoulli

In [1,2], an approximate continuous relaxation of the Bernoulli distribution is introduced as follows: $$X = \frac{1}{1 + e^{- (\theta - L) / \tau}}$$ where $L$ is a Logistic random variable, $\tau&...
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31 views

Normalizing model output in a binary classifier

In some cases, the business wishes to have the scores from a binary classifier normalized around a specific value. Are then general methods to apply this normalization? If we have a subset of ...
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1answer
26 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 ...
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26 views

Parametric shared frailty models with individual monotone yet population non-monotone hazard

I'm fitting parametric survival models with/without shared frailty on individuals. The hazard in my data is very low at first, then increases and finally decreases again, sort of a bell shaped curve. ...
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2answers
203 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 ...
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34 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 ...
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31 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 ...
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1answer
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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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2answers
559 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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36 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)}{(\...
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1answer
71 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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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 ...
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2answers
213 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 ...
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155 views

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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1answer
239 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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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 ...
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1answer
259 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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1answer
856 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-...
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72 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 (...
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2answers
192 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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3answers
2k 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?
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184 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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1answer
499 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 ...
43
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4answers
34k 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
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1answer
215 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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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 ...
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1answer
231 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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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 ...