Questions tagged [logistic-distribution]
A symmetric distribution which CDF is the logistic function.
55
questions
9
votes
1
answer
750
views
What is the specific name of this distribution?
I just can’t seem to find the name of this distribution:
$$\frac{e^{-x}}{(1+e^{-x}) ^2}.$$
From my understanding, it is generally applied to pandemics/epidemics.
None of the statistics books that I ...
0
votes
0
answers
30
views
How to linearize logistics function? [closed]
The function is $y=L/(1+e^{(-kx)} )$. After research I found this equation to linearize it, replace y values by this: $\ln(1/(y/(L-1)))$ , then keep x values the same and plot it. But with further ...
- 1
3
votes
1
answer
64
views
Approximating the standard normal density with the logistic density: How to numerically optimize $\infty$-norm?
Let's say that we want to use the logistic distribution as an approximation to the standard normal density. As the location parameter of the logistic distribution is $0$, the scale parameter $s$ is ...
- 29.5k
1
vote
0
answers
25
views
Plotting custom logistic distribution
I'm trying to understand the logistic distribution and its application in a sports scoring model.
The CDF of the logistic distribution is:
$F(x) = {1 \over 1 + e^{-(x-\mu) / s}}$
I can then use ...
1
vote
0
answers
20
views
Need guidance to fit logistic distributions to compare performances in multiple events
Ok, here's the thing. I'm trying to compare performances in different running events (i.e. all registered performances in each event from 1990 to 2023), to estimate equivalent performances. After ...
2
votes
1
answer
126
views
How to evaluate a Logistic Regression?
There are some previous post treating how to validate a logistic regression: Source 1 and Source 2.
But, still, those threads does not answer my question.
Therefore:
If a logistic regression predict ...
- 175
2
votes
0
answers
97
views
Logistic regression - Confidence interval for x axis
My question is very similar to the post Confidence interval for x-values given a probability in a logistic regression
where ultimately no answer was given. I have also posted a similar version on the ...
- 21
5
votes
1
answer
630
views
Where does the Logistic Distribution get its name?
Having read around on the topic I understand its application as a close approximation of the normal distribution with a nicer mathematical form, but where does its name come from?
Is it associated ...
- 451
1
vote
0
answers
177
views
Multinomial Logistic Regression as a latent variable model
I was reading the wiki entry for multinomial logistic regression https://en.wikipedia.org/wiki/Multinomial_logistic_regression#As_a_latent-variable_model
and it states that we can view the multinomial ...
- 11
0
votes
2
answers
900
views
Logistic distribution's minimal sufficient statistics
Distribution function (pdf) is
$$f(x|\theta) = \frac{e^{-x-\theta}}{(1+e^{-(x-\theta)})^2},~-\infty<x<\infty,~-\infty<\theta<\infty$$
If $x$ is sample from population, $f(x|\theta)$ is
$$ ...
3
votes
2
answers
865
views
Why does the glm function converge and not give an error when all y's are equal to the same value?
I need to fit a univariate logistic model with few observations (between 10 and 20).
In some cases, y is equal to the same value (example 1) for all observations.
Theoretically, the model should not ...
- 163
2
votes
2
answers
343
views
Inverse Mills Ratio for Logit?
For $X\sim N(\mu,\sigma^2)$ ,
$$E[X|X>\alpha] = \mu +\sigma \frac{\phi\left(\frac{\alpha-\mu}{\sigma}\right)}{1-\Phi\left(\frac{\alpha-\mu}{\sigma}\right)} $$
Is there an analogous expression for ...
- 140
1
vote
1
answer
200
views
Is the Hodges-Lehmann estimator 'optimal' for estimating the location parameter of Logistic distribution?
Is the Hodges-Lehmann estimator $\hat\theta_{HL}=\operatorname{median}\limits_{1\le i\le j\le n}\left\{\frac{X_i+X_j}{2}\right\}$ in some sense 'optimal' for estimating the location parameter $\theta$ ...
- 10.7k
0
votes
0
answers
80
views
Are their feature selection always go by linear model?
A generalized linear model maps a linear transformation of features to some response through monotonic function, does GLM feature selection always go by analyzing the coefs of this linear ...
- 1,007
2
votes
1
answer
187
views
Trade-off between omitting variables or dropping observations in multivariate logistic regression
Say you are selecting $n$ observations from a complex survey of $N$ individuals to create an analytical sample of relevant observations; and that you intend to fit a binomial multivariate logistic ...
- 23
0
votes
1
answer
793
views
What are the preliminary analysis before running a logistic regression?
I have a dichotomous variable which represents if a student is accepted or not in a University. In order to do this I have about 60 variables (information of the students: gender, age, etc; their ...
- 31
3
votes
2
answers
72
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 ...
- 3,271
0
votes
1
answer
259
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 ...
- 233
0
votes
1
answer
433
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 ...
- 45
4
votes
1
answer
140
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$$
have for $c&...
- 264
0
votes
1
answer
211
views
Relation between logistic regression and logistic distribution [duplicate]
When we are using logistic regression, we can get the probability that $y$ belongs to class $1$ as follows:
$P(y=1|x;\theta)=\frac{1}{1+\exp(-\theta^Tx)}$.
PDF of a logistic distribution is given as ...
- 473
2
votes
1
answer
469
views
A Gaussian scale mixture representation of the logistic distribution
Can the logistic distribution with density function
$$f(x) = \frac{e^{-x}}{\left(1 + e^{-x}\right)^2}$$
be represented as a Gaussian scale mixture? In other words, if
\begin{align*}
X|V &\sim N(0, ...
- 7,047
0
votes
1
answer
33
views
What is (are) scenerios and practical settings that can possibly lead to the weibull-log-Logistic mixture distribution?
In my paper I studied Weibull-loglogistic mixture distributions in reliability and life testing, some structural properties of the model are presented including moments, reliability, hazard rate ...
1
vote
0
answers
106
views
What are assumptions for logistic binomial regression if all independent and independent variables are dichotomous?
I have three independent and one dependent variables of the dichotomous type and I am trying to use logistic binomial regression. I have 117 observations in total.
When I read the literature, some of ...
- 153
0
votes
1
answer
55
views
logistic distribution
Is it true that almost every discrete data set containing positive values follow logistic distribution if the data set is log-transformed and standardised(subtracting mean and dividing by standard ...
1
vote
1
answer
1k
views
What form of conjugate prior best fits this likelihood distribution? [closed]
Joint likelihood of a two part model consisting of logistic regression and log-normal model:
- 11
2
votes
1
answer
147
views
Change of variable for logistic distribution to loglogistic - where do I go wrong?
Similar to what I described in this post I would like to make the following change of variable $$Y := \exp( \eta + \sigma e ), \sigma>0 $$ where $e$ has the standard logistic density $f_E(e) = \exp(...
- 6,412
4
votes
1
answer
2k
views
Comparison of logit and probit estimations
There are a lot of questions concerning logit and probit relations (led by 20523), but I'm still confused with a seemingly simple issue.
On the one hand, often we see that for 'rule-of-thumb' ...
- 337
1
vote
1
answer
173
views
How to invert a mixture of log-logistic distributions? [duplicate]
Say I have a CDF of the form
$$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 ...
- 113
0
votes
1
answer
31
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 ...
- 163
5
votes
2
answers
3k
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 ...
1
vote
1
answer
129
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 ...
- 51
0
votes
0
answers
220
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 ...
- 1
2
votes
1
answer
106
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 ...
- 264
1
vote
0
answers
41
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 ...
- 517
8
votes
2
answers
3k
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
0
answers
54
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)}{(\...
- 535
3
votes
2
answers
741
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 ...
- 435
1
vote
1
answer
192
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 ...
- 13
4
votes
3
answers
7k
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 ...
- 41
1
vote
2
answers
761
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 ...
- 11
0
votes
1
answer
522
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)$...
- 115
0
votes
1
answer
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 ...
- 1
1
vote
1
answer
309
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 ...
- 796
2
votes
1
answer
3k
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}}$$
Does $f(x)$ belong to the exponential family?
My solution is
$\exp[(-2)\cdot \ln(1+\exp\{-x-θ\})-x-...
- 63
1
vote
0
answers
89
views
Calculate sample mean confidence interval of noisy logistical distribution
I have $n$ samples which follow a logistic distribution with unknown $u$ and $s$; it is affected by a Gaussian noise with 0 mean.
I would like to estimate its average $u$ with a confidence interval (...
- 111
1
vote
2
answers
289
views
t-test with logistic and Gumbel distributions
I know that one of the basic assumptions of a t-test is that the data is drawn from a Gaussian distribution.
Using an Anderson-Darling test, I've found that the datasets I am working with are either ...
- 11
28
votes
3
answers
4k
views
Why is the logistic distribution called "logistic"?
What is "logistic" about the logistic distribution, in a common sense way? What is the etymology of and the lexical rationale for the name, not just pure math definition?
- 383
1
vote
0
answers
197
views
Find an unbiased estimator from a random sample from the logistic distribution
So I'm not sure where to start on this one, so any hints will help me because I'm a little lost on finding unbiased estimators. So suppose $X_1, X_2,... X_n$ is a random sample from the logistic ...
- 61
3
votes
1
answer
778
views
Obtaining the Log-logistic distribution from a truncated logistic distribution
Let $$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 ...
- 149