Growth of tuber crops and almost sure band for quantiles

ABSTRACT

Some tuber crops are governed by memoryless property of exponential distribution leading to a mixture distribution with heavy tail. Quantile-based estimators may then be appropriate than mean as a measure of central tendency. We prove almost sure representation theorems for sample quantiles in a general setup of U statistics, under slightly stronger assumption than assuming the existence of a continuously differentiable distribution function F for the kernel h. We obtain almost sure (a.s.) upper and lower estimate for F^{− 1}(p), p ∈ (0, 1) as a band for p varying. As an application, dataset arising from two varieties of potato cultivation are analyzed.

KEYWORDS:

• Elephant foot yam
• Growth model
• Mixture of exponential density
• One-sided estimation
• Quantiles
• U-statistics

Mathematics Subject Classification:

• Primary 62E15
• secondary 62P99

Acknowledgments

Thanks are due to the referee for constructive comments that improved the presentation.