On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables

Statistical Papers

Volumn 54, Issue 2, 2013, Pages 309-323

  Díaz Francés, Eloísa ^a   Rubio, Francisco J ^b  

^a CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS   (Mexico)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Coefficient of variation; Ratio of normal means; ROC curve

Indexed keywords

EID: 84876094891     PISSN: 09325026     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00362-012-0429-2     Document Type: Article

References (16)

1. Brody JP, Williams BA, Wold BJ, Quake SR (2002) Significance and statistical errors in the analysis of DNA microarray data. Proc Natl Acad Sci USA 99: 12975-12978.
2. Chamberlin SR, Sprott DA (1987) Some logical aspects of the linear functional relationship. Stat Pap 28: 291-299.
3. Díaz-Francés E, Sprott DA (2001) Statistical analysis of nuclear genome size of plants with flow cytometer data. Cytometry 45: 244-249.
4. Geary RC (1930) The frequency distribution of the quotient of two normal variates. J R Stat Soc B Methodol 93: 442-446.
5. Hayya J, Armstrong D, Gressis N (1975) A note on the ratio of two normally distributed variables. Manag Sci 21: 1338-1341.
6. Hinkley DV (1969) On the ratio of two correlated normal variables. Biometrika 56: 635-639.
7. Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific Publishing, River Edge.
8. Kuethe DO, Caprihan A, Gach HM, Lowe IJ, Fukushima E (2000) Imaging obstructed ventilation with NMR using inert fluorinated gases. J Appl Physiol 88: 2279-2286.
9. Lisák MA, Doležel J (1998) Estimation of nuclear DNA content in Sesleria (Poaceae). Caryologia 52: 123-132.
10. Marsaglia G (1965) Ratios of normal variables and ratios of sums of uniform variables. J Am Stat Assoc 60: 193-204.
11. Marsaglia G (2006) Ratios of normal variables. J Stat Softw 16: 1-10.
12. Merrill AS (1928) Frequency distribution of an index when both the components follow the normal law. Biometrika 20A: 53-63.
13. Palomino G, Doležel J, Cid R, Brunner I, Méndez I, Rubluo A (1999) Nuclear genome stability of mammillaria San-Angelensis (Cactaceae) regenerants. Plant Sci 141: 191-200.
14. Schneeweiss H, Sprott DA, Viveros R (1987) An approximate conditional analysis of the linear functional relationship. Stat Pap 28: 183-202.
15. Sklar LA (2005) Flow cytometry for biotechnology. Oxford University Press, New York.
16. Watson JV (1992) Flow cytometry data analysis: basic concepts and statistics. Cambridge University Press, New York.