Related papers: Relieving and Readjusting Pythagoras
Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its…
Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton and Johnson, 1969; Pearson, 1895; Solomon and Stephens, 1978). Thus, Pearson distributions made statistical analysis…
Recently, Lee and Cha (2015, `On two generalized classes of discrete bivariate distributions', {\it American Statistician}, 221 - 230) proposed two general classes of discrete bivariate distributions. They have discussed some general…
Let $\mathcal{A}$ be a Las Vegas algorithm, i.e. an algorithm whose running time $T$ is a random variable drawn according to a certain probability distribution $p$. In 1993, Luby, Sinclair and Zuckerman [LSZ93] proved that a simple…
Regression is a fundamental tool in scientific research. Ordinary least squares (OLS), one of the most widely used regression methods, enjoys several desirable properties, including the best linear unbiased estimator (BLUE) property. It is…
Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…
We develop a maximum likelihood estimating approach for time-to-event Weibull regression models with outcome-dependent sampling, where sampling of subjects is dependent on the residual fraction of the time left to developing the event of…
According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…
The National Basketball Association (NBA) imposes a player salary cap. It is therefore useful to develop tools to measure the relative realized return of a player's salary given their on court performance. Very few such studies exist,…
In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes…
Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…
The payoff in the Chow-Robbins coin-tossing game is the proportion of heads when you stop. Knowing when to stop to maximize expectation was addressed by Chow and Robbins(1965), who proved there exist integers ${k_n}$ such that it is optimal…
To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…
Evolutionary dynamics provides an iconic relationship --- the periodic frequency of a game is determined by the payoff matrix of the game. This paper reports the first experimental evidence to demonstrate this relationship. Evidence comes…
Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape $\alpha$ and scale $\beta$. In this study, bimodality…
Balls-and-bins games have been a wildly successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a…
The setting of the classic prophet inequality is as follows: a gambler is shown the probability distributions of $n$ independent, non-negative random variables with finite expectations. In their indexed order, a value is drawn from each…
Gradient Boosting Machines (GBM) are hugely popular for solving tabular data problems. However, practitioners are not only interested in point predictions, but also in probabilistic predictions in order to quantify the uncertainty of the…
For a game with positive expectation and some negative profit, a unique price exists, at which the optimal proportion of investment reaches its maximum. For a game with parallel translated profit, the ratio of this price to its expectation…
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum…