# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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### Modelling losses in insurance - why nobody seems to talk about left-truncated distribution?

In the (re)insurance field, it is quite common to simulate losses via a Monte Carlo approach and a stochastic generator of both frequency and severity individually (independency between both being ...
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### Computing the inverse Beta cdf in R [closed]

In MATLAB, the function betainv(P, A, B) computes the beta CDF inverse with parameters A and B specified for the corresponding probabilities in P. Is there a similar function in R that can do the same?...
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1 vote
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### Does there exist any causal explainability tool for NNs?

Say I have a neural network which has 1,000,000 parameters built using 100 features and I wish to understand the underlying data-generating process for how the model arrived at each prediction. Simply ...
• 11
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### Logistic regression: What are use cases for logistic regressions where $n \neq 1$, i.e., $n >1$? [duplicate]

NOTE: This question relates to Binomial logistic regression. Thus, the $n$ in the title, refers to the parameter of the Binomial distribution. Most real-world use cases of logistic regression ...
7 views

### Entropy discribe sample with less data bias? [closed]

Say if we work in youtube.we want to analysis user prefrence for movie. If user A only watches two thrill movie,then entropy would be 1*log(1)=0. If user B watches two movie,a comedy and aa thrill,...
1 vote
26 views

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### How do I calculate the expected values if the correlation coefficients are -1/0/+1? [closed]

How do I calculate the expected values if the correlation coefficients are -1/0/+1? I know that -1 means backwards correlation and so on but I just need an example.
1 vote
36 views

### Can I take the p-value from a probability table for a modified z-score, just like a z-score?

I have a question regarding the modified Z-score, can I use this score in a Z-probability table, i.e. the p-value from a modified z-score? where: z-score = (xi - μ)/σ (the z-score probability can be ...
23 views

### How can I back transform a log data to interpret t-test and get original CI?

I have data that is not normally distributed. I can log-transform it to be normally distributed, and then perform a t-test and get confidence intervals (CI). But how do I interpret the results of the ...
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1 vote
68 views

### How to show that $X_n + Y_n \to X + Y$ holds in the $L^1$ norm?

Let $X_n$ and $Y_n$ be sequences of random variables. Show that $X_n + Y_n \to X + Y$ (1) $X_nY_n \to XY$ (2) If $\mathbb{P}(X=0) = 0, \; \frac{Y_n}{X_n} \to \frac{Y}{X}$ (3) are true for convergence ...
55 views
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### Value of $E[X^T A X B X^T CX]$ for Gaussian matrices $X$?

Suppose $X$ is an $m\times n$ random matrix where rows $x$ are I.I.D. samples of $n$-dimensional Gaussian, and $A,B,C$ are matrices of appropriate dimension. What is the value of the following matrix? ...
• 5,627
1 vote
33 views

### How to derive the F statistic from likelihood ratio test

I am trying to test whether sigma1 is different from sigma 2 (2 ind samples that follow a normal dist) and I have no idea how to use the likelihood ratio to derive the F statistic that tests this.
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### Show that for a squared error loss function L(^θ, θ) = (^θ - θ)^2, the mean of the posterior distribution is the best estimate for the parameter θ [closed]

Show that for a squared error loss function L(^θ, θ) = (^θ - θ)^2, the mean of the posterior distribution is the best estimate for the parameter θ. I'm literally lost on this question, if anyone could ...
• 1
20 views

### Compare distributions after transforming from continuous to discrete [closed]

I have two variables: X and Y. X variable (varies between 0 and 300) is continuous and Y with same range of variation but is discrete and have 3 classes (0-100, 100-200 and 200-300), which is pretty ...
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### Standard errors from zero vs. actual standard error value

Obviously a standard error value close to zero is more desirable. However, is there a rule of thumb for how many standard errors AWAY from zero is considered good or acceptable? Does this also change ...
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### How does center variable help address multicollinearity problems for interaction with polynomial terms

I hope someone can help me better understand how center variables can help address the problem of multicollinearity problem when the regression includes interactions with polynomial terms. My ...
11 views

### How do I determine a noise distribution? [closed]

Let’s say we have a set of instances $X={x_1, x_2, ..., x_n}$ whose distribution is unaware, but the mean and var values can be calculated. Now we add a noise generated from a certain distribution (...
11 views

### Random Variables as Function of Correlation Coefficient [closed]

If we have that $X, Y\~N(0, 1)$ and that $Corr(X, Y)=\rho$, how can we write $Y$ as a function of $X?$
20 views

### To check if the churn probability score from old and new model is similar

I have calculated the churn probability score for every customer id using glm model. So, I have a data frame with every customer id and its churn probability score. Ex cust_id 1 has a score of 0.11 ...
1 vote
20 views

### Standard error logic

Obviously the closer the standard error to zero the better. However, what if the values the in which the standard errors are from are extremely large and the standard errors are much higher than zero ...
• 11
34 views

### Binomial to Poisson Approximation

So, a little context. The image you see is from the GCE A-LEVEL syllabus where they have defined the conditions for approximating binomial to poisson. But why did they have mention that the ...
112 views

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### Structural Causal Models with cycles

I this context I am referring to Structural Causal Models (SCM) such as presented here https://fabiandablander.com/r/Causal-Inference.html or here https://medium.data4sci.com/causal-inference-part-iv-...
22 views

### Jenks Natural breaks - Interpreting Goodness of Variance Fit

I am trying to find breaks in a multiple continuous type variables. So, I tried the jenks natural breaks algorithm. Based on the code from here, I managed to find ...
• 2,096
27 views

### How to compare the mean to the mean of mean values of dummy variables?

I am trying to validate the calculations of a mean value for a collection of binary variable values. The validation process is where I compare x to y where: x is the mean value of percentage of ...
11 views

### Statistical Test of the significance of difference between 2 ordered columns

I'm trying to come up with an appropriate statistical test for the significance of the difference between 2 ordered columns A = [a0, a1, ..., aN] and B = [b0, b1, ..., bN]. Each of the columns is of ...
2k views

13 views

### Chapter 5 political stats [closed]

(5 points) Imagine that you are a researcher, and that as part of your research you need to gauge the favorability of free lunch programs within the county school districts. During your research, you ...
1 vote
22 views

### Variance of inverse RV

I am trying to find variance of Y=1/(1+abs(x)) where X is Gaussian RV with mean m, var sigma^2To do that my initial step is to find MGF. can anyone give me ...
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15 views

### about the derivative of the characteristic function of the Poisson distribution [closed]

I do not understand why differentiation of the above equation leads to the below equation. Can you please tell me?
2k views

### What are some good blogs for Mathematical Statistics and Machine Learning?

I am looking for blogs that focus on the mathematical theory of Statistics and Machine Learning, ideally at a research or "advanced" level. The blog doesn't have to be solely about these ...
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### I need help clarifying what (R1,..RN) is in this context

Let R be the space of all the N! permutations of (1,2, ..., N), and let R = (R1,...RN) be uniformly distributed over R. The thing i don't understand is what "R = (R1,...RN) be uniformly ...
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1 vote
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### Backend process of lmer function [closed]

I am trying to learn mixed models using lmer function and I am able to use it. But I am not able to understand what is going on in the backend like how it is taking care of fixed effects and random ...