Kernel Smoothed Probability Mass Functions for Ordered Datatypes

Ordered Probability Mass Function

Suppose that in the four tests Alice’s scores are 90, 95, 85, 90, and Bob’s scores are 85, 95, 90, 90. How to evaluate their scores? In this paper, we introduce the concept of ordered probability mass function which can be used to find a probability mass function with smaller variance. More interestingly, we can use it to distinguish sequences of positive numbers statistically.

Probability Generating Functions for Sattolo’s Algorithm

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...

Processes, Functions, and Datatypes

Based on a name-passing calculus and on its typing system we show how to build several language constructors towards strongly-typed concurrent programming languages. In particular, we introduce a notion of datatype declaration , and show how to create values of a datatype and how to take such values apart. Further expressions include a form of abstraction and of application. Expressions evaluat...

Kernel smoothed prediction intervals for ARMA models

Abstract The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on the sample forecast errors. In this paper we apply nonparametric quantile regression to the empirical forecast errors using lead t...

Kernel smoothed prediction intervals for ARMA models