## Solved – Student t-distribution parameter/s and MLE

So I always thought of the Student t-distribution as having only 1 parameter, v, the degrees of freedom (as described by wikipedia). When I searched however on how to find the MLE of v I keep coming across questions mentioning mu and sigma as parameters as well. So 1) Is the Student-t Distribution a special … Read more

## Solved – Evaluating relative accuracy/error for continuous value prediction (and assessing relative average difference/error)

I was trying to understand what are good (or standard) way of evaluating relative accuracy for continuous data. Say for example, say I have some statistical algorithm S that outputs some real number from a vector of data. Something like \$S:mathbb{R}^k mapsto mathbb{R}\$ Intuitively what I am interested in finding is a measure of how … Read more

## Solved – Inventory control – first order quantity of periodic order quantities model

I Have read "Manufacturing Planning and Control for Supply Chain Management 6th Edition" by F.Robert Jacobs. I found the problem on the Periodic Order Quantities (POQ). As I know POQ calculation is after calculate the Economic Order Quantity (EOQ). In the book contained an example problem : To calculate EOQ from the above data using … Read more

## Solved – Inventory control – first order quantity of periodic order quantities model

I Have read "Manufacturing Planning and Control for Supply Chain Management 6th Edition" by F.Robert Jacobs. I found the problem on the Periodic Order Quantities (POQ). As I know POQ calculation is after calculate the Economic Order Quantity (EOQ). In the book contained an example problem : To calculate EOQ from the above data using … Read more

## Solved – How to develop a dataset for the gravity model of international Trade

The gravity model of International trade is used to estimate the determinants of bilateral trade between countries. In developing the dataset for the gravity model, do i need to manually pair the countries in terms of total value of exports/imports and the distance or i just need to enter them one by one with their … Read more

## Solved – Maximum likelihood estimation in a Poisson model for football (soccer) scores

I've got a set of football results and I want to make a probabilty model of football scores as described in Dixon, Coles (1997, http://www.math.ku.dk/~rolf/teaching/thesis/DixonColes.pdf). They estimate the parameters based on maximum likelihood and the model assumes the variables are independent Poisson. Now I have 2 questions: How should I transform my data to input … Read more

## Solved – Is the sample mean a better point estimate of the population median than the sample median

A beginner's question to check I've understood correctly. A basic stats textbook says: "The variance of the sampling distribution of the median is greater than that of the sampling distribution of the mean. It follows that sample mean is likely to be closer to the population mean than the sample median. Therefore, the sample mean … Read more

## Solved – Deriving likelihood function of binomial distribution, confusion over exponents

This question focuses on a specific aspect of this one: How to derive the likelihood function for binomial distribution for parameter estimation? In my own derivation, I start with: \$\$f(xmid p) = mC_x~p^x(1-p)^{m-x}\$\$ Ignoring \$mC_x\$, the likelihood function is then given by: \$\$L(p) = prod_{i=1}^np^{x_i}(1-p)^{m-x_i} = p^{sum_1^n x_i}(1-p)^{sum_1^n m-x_i} = p^{x}(1-p)^{nm-x}\$\$ However, in the question … Read more

## Solved – Maximum likelihood estimation and the n-th order statistic

Let \$X_1, …, X_n\$ be a sample of independent, identically distributed random variables, with density \$\$ f_{theta}(x)=e^{ (theta -x)}\$\$. \$x ge theta\$, otherwise \$f_theta = 0\$ The question is: Determine the maximum likelihood estimator \$hat{theta}_n\$ of \$theta\$. I don't understand this question. What exactly does \$hat{theta}_n\$ mean? Wikipedia says something about the nth order statistic: … Read more

## Solved – ARMA/GARCH estimation in sequence

I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with the auto.arima model in the forecast package in R and a GARCH model on the residuals of the ARIMA model. Is … Read more