Abstract
This book is concerned with making inferences about parameters of probability distribution functions. An inference is a generalization made from some specific observations. The specific observations are the data; the generalization is about the values of the parameters. The data are presumed to be a (relatively) small subset of values obtained, measured, or observed in some way from a larger population (sample space). Generally, the parameters are unknown. What we have instead are sample statistics, which are functions of the data. These statistics are themselves random variables, in that every new subset of values from the population yields potentially at least a new value for the statistic. As a result, the sample statistic also has a sample space associated with it, and a probability distribution function as well. The probability distribution function for a sample statistic is often referred to as a sampling distribution function (Meyer 1970). The form of the sampling distribution usually depends on the formula for the statistic, and the distribution function of the random variable for which the data constitute a subset of values or observations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bickel, P. J., & Doksum, K. A. (2007). Mathematical statistics: Basic ideas and selected topics (2nd ed., Vol. 1). Upper Saddle River, NJ: Pearson Prentice Hall.
Desu, M. M., & Raghavarao, D. (1990). Sample size methodology. San Diego, CA: Academic.
Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. Philadelphia: SIAM.
Meyer, P. L. (1970). Introduction to probability and statistical applications (2nd ed.). Boston: Addison-Wesley.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Pardo, S.A. (2016). Some Statistical Concepts. In: Empirical Modeling and Data Analysis for Engineers and Applied Scientists. Springer, Cham. https://doi.org/10.1007/978-3-319-32768-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-32768-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-32767-9
Online ISBN: 978-3-319-32768-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)