Handbook of Tables for Order Statistics from Lognormal Distributions with Applications

Softcover Nachdruck of the original 1. Auflage 1999
ISBN: 978-0-7923-5712-4
Verlag: Springer US

Buch, Englisch, 868 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1311 g

Lognormal distributions are one of the most commonly studied models in the sta­ tistical literature while being most frequently used in the applied literature. The lognormal distributions have been used in problems arising from such diverse fields as hydrology, biology, communication engineering, environmental science, reliability, agriculture, medical science, mechanical engineering, material science, and pharma­ cology. Though the lognormal distributions have been around from the beginning of this century (see Chapter 1), much of the work concerning inferential methods for the parameters of lognormal distributions has been done in the recent past. Most of these methods of inference, particUlarly those based on censored samples, involve extensive use of numerical methods to solve some nonlinear equations. Order statistics and their moments have been discussed quite extensively in the literature for many distributions. It is very well known that the moments of order statistics can be derived explicitly only in the case of a few distributions such as exponential, uniform, power function, Pareto, and logistic. In most other cases in­ cluding the lognormal case, they have to be numerically determined. The moments of order statistics from a specific lognormal distribution have been tabulated ear­ lier. However, the moments of order statistics from general lognormal distributions have not been discussed in the statistical literature until now primarily due to the extreme computational complexity in their numerical determination.

Zielgruppe

Research

Autoren/Hrsg.

Chen, W. S.

Balakrishnan, N.

Fachgebiete

• Technische Wissenschaften Bauingenieurwesen Bauingenieurwesen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik Industrielle Qualitätskontrolle
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Technische Wissenschaften Technik Allgemein Technische Zuverlässigkeit, Sicherheitstechnik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik

Inhaltsverzeichnis

1. Introduction and Historical Remarks.- 2. Lognormal Distributions and Properties.- 3. Order Statistics and Moments.- 4. Best Linear Unbiased Estimation of Location and Scale Parameters.- 5. Illustrative Examples.- 6. Best Linear Unbiased Prediction.- 7. Quantile-Quantile Plots and Goodness-of-Fit Test.- Figures.- Tables.