Growth curve of elephant-foot-yam, plant stress and Mann-Whitney U-statistics

Document Type

Conference Article

Publication Title

Springer Proceedings in Mathematics and Statistics

Abstract

Longitudinal growth of Elephant foot yam [Amorphophallus paeoniifolius (Dennst.) Nicolson] is studied for different seed weights by taking plants off the ground for interim growth measurements by Archimedean principle, and then replanting these to continue growth experiment till maturity at the Indian Statistical Institute, Giridih farm. In order to find appropriate seed weight for high yield and appropriate time for harvest, twenty yam plants in each category of seed weight 500, 650 and 800 g are considered in a growth experiment conducted in the year 2013. Effect of severe plant stress on growth is also examined when underground yam is detached from a plant, while pulling stems off the ground by jerk in the middle of experiment, thus endangering plant survival during interim growth recording. The injured plant having only stem structure survived when replanted under stress, and deposited yam in its extended lifetime. Under stress, canopy radius of yam plant is a more stress-sensitive variable compared to perimeter on the stem top. These variables may be modeled by normal distribution. Yam plant can withstand severe stress, and over time may grow like a healthy plant when proper care is taken. Deviations of observed data from estimated growth curve are modeled by Ornstien-Uhlenbeck process, a Gaussian process with exponentially decaying correlation function. Process parameters are estimated from the real data set and comparison of residual variability over seed weights is made to ascertain assured yield for a given seed weight. Under the assumption of symmetric error distribution, growth curves are estimated; and the proposed new technique is compared with general nonparametric regression. Among different seed weights, growth curve of yam yield corresponding to seed weight 650 g is seen to be superior from almost sure confidence band. Mann-Whitney U test indicates the same, the test statistic is further considered to compare the induced plant stress due to uprooting and replanting that affects slope change in canopy radius around the time of intervention for interim growth recording of yam. Error bounds for two sample U-statistics from its projection under stringent moment assumptions on kernel are obtained to ascertain the adequacy of the test statistics.

First Page

1

Last Page

41

DOI

10.1007/978-3-319-63886-7_1

Publication Date

1-1-2017

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