# Questions tagged [mathematical-statistics]

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

4,201 questions
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### Find the same components between two distributions

GMM assumes that a distribution consists of multiple Gaussian Distributions. Is it possible to find the same components between the two distribution? For example, there are two distribution D1 and D2. ...
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### Monte Carlo simulation from autocorrelated empirical distribution

So I'm trying to perform a Monte Carlo simulation an empirical distribution of log-return time series data. However, Ljung-Box test indicates that there is significant autocorrelation at multiple lags....
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### Why does the cumulative distribution function for discrete random variable right continuous?

If the random variable is discrete, then the cumulative value should also be discrete because the variable can only take on discrete values, right?
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### Introductory books on bayesian statistics with focus on normal distribution

I am searching for introductory books on bayesian statistics. Which Focus on normal distribution (Most of the books I came across through this answer focus on binomial distribution) Practical ...
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### Distribution of a one realization of a stochastic process [closed]

Suppose $X$ is a stochastic process such that $X(t) \sim N\left(\mu(t), \sigma^2(t)\right)$ for all $t$ and $\mu$ and $\sigma$ are some smooth functions and we are given one realization of this ...
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### Question about prediction: if a variable can predict another variable [closed]

I have a question about the prediction. This question stopped me for a whole afternoon, still do not have an idea on how to solve it. Would you please give me a clue. The question is: ...
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### How to show that the error variance of the best linear predictor is inferior to the proportional predictor?

Let's consider the 1D case. How do we prove that the error variance of the Best Linear Predictor (BLP) is inferior than the Proportional Predictor (i.e. the Linear Predictor without the intercept)? ...
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### Calculating variance of process with time-varying variance

This is a question stemming off a previous post I had regarding calculating portfolio volatility. For a portfolio consisting of multiple assets, I understand that there are multiple ways to calculate ...
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### Calculating portfolio volatility from portfolio returns vs. from covariance matrix

I'm having trouble understanding the difference in calculating portfolio volatility via the portfolio returns vs. via the covariance matrix. To be more specific: I understand that on the individual ...
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### Statistics and Probability. Please show solution [closed]

Miss Romero noted that the mean scores of a random sample of 15 grade 8 students who had taken a special test were 80.5. If the standard deviation of the scores was 3.1 and the sample came from an ...
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### OLS with ARMA errors, tip or two

I need a tip or two. I am performing OLS with dynamic factors (4x1 factors each representing a PANEL of 24 series, hence 4 time series). My OLS has autocorrelation in the error so I want to use OLS ...
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### Principle coordinates analysis - visualization and assigning text to graph in r [closed]

I've recently run a principle coordinates analysis in r with ~ 200 subjects and 17 binary variables. I've plotted my points successfully, the challenge I'm facing is that when I plot the text with the ...
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### Proof for simulation of NHPP by thinning

Background: I'm trying to show equivalency between the density function for a non-homogenous exponential process (NHEP?), (i.e. the arrival times of events generated by a non-homogenous Poisson ...
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### Marketing Funnel Percentage Calculations

I implement a marketing funnel in python and I have an issue around the topic that I can't solve neither in statistical level. Lets say that we have the funnel A which contains ...
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