Density of the Ratio of Two Normal Random Variables and Applications

DOI10.1080/03610920600683689zbMath1105.62018OpenAlexW1969278343WikidataQ30047522 ScholiaQ30047522MaRDI QIDQ3424181

Éric Marchand, Thu Pham Gia, Noyan Turkkan

Publication date: 15 February 2007

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610920600683689

zbMATH Keywords

integral representationHermite functionnormalratiobivariate normalfinite samplingKummer confluent hypergeometric functions

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Characterization and structure theory of statistical distributions (62E10) Applications of hypergeometric functions (33C90) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (17)

On comparison of relative growth rates under different environmental conditions with application to biological data ⋮ Fat tails arise endogenously from supply/demand, with or without jump processes ⋮ Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters ⋮ Designing the Scale Counting Procedure for Large Numbers of Small Parts ⋮ Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean ⋮ Cauchy, normal and correlations versus heavy tails ⋮ Convexity and monotonicity in language coordination: simulating the emergence of semantic universals in populations of cognitive agents ⋮ A class of ratio distributions of dependent folded normals and its applications ⋮ Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts ⋮ Bayesian analysis of a 2×2 contingency table with dependent proportions and exact sample size ⋮ The Use of Ratios to Compare Volatilities and VaRs ⋮ The direct integral method for confidence intervals for the ratio of two location parameters ⋮ Construction of confidence intervals for the Laspeyres price index ⋮ Parameter estimation for Gaussian mean-reverting Ornstein–Uhlenbeck processes of the second kind: Non-ergodic case ⋮ Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model ⋮ Statistical inference for nonergodic weighted fractional Vasicek models ⋮ Asymptotic analysis of synchrosqueezing transform -- toward statistical inference with nonlinear-type time-frequency analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Conditional distributions and the bivariate normal distribution
• The hazard rate of the power-quadratic exponential family of distributions
• Multiple Hypergeometric Functions: Probabilistic Interpretations and Statistical Uses
• The probability distribution of the ratio of the absolute values of two normal variables
• Distributions of ratios of random variables from the power-quadratic exponential family and applications
• THE DISTRIBUTION OF THE INDEX IN A NORMAL BIVARIATE POPULATION
• Mathematical Statistics
• Ratios of Normal Variables and Ratios of Sums of Uniform Variables
• On the ratio of two correlated normal random variables
• Non‐normal bivariate densities with normal marginals and linear regression functions *
• A NOTE ON NORMAL CORRELATION
• A Note on the Estimation of Some Mean Values for a Bivariate Distribution
• THE PROBABILITY INTEGRAL FOR TWO VARIABLES

This page was built for publication: Density of the Ratio of Two Normal Random Variables and Applications