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ThesisItem Open Access Pattern of occurrence of rainfall and estimation of rainfall probabilities in northern districts of Kerala(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1987) Santhoh, K; KAU; Prabhakaran, P VA study was undertaken with a view to characterize the pattern of occurrence of rainfall and to estimate the rainfall probabilities and confidence limits at six reporting stations of the northern districts of Kerala viz, Kasaragod, Irikkur, Cannanore, Kozhikode, Quilandy and Mananthody, Daily rainfall data of the past 30 years were used to investigate the pattern of fortnightly and seasonal rainfall occurrence by fitting a first order Markov chain model to the sequence of wet and dry days. The rainfall probabilities and confidence limits were computed by fitting appropriate probability distributions to fortnightly rainfall amounts. The results of the analysis showed that at all the centres, there were more chances for a wet day to be preceded by a wet day than by a dryday. The maximum expected length of wet spell at different centres was observed during 12th to 14th fortnight of the year. The state occupation probability at equillibrium for a wet day was also foundmaximum during the same period. It could be seen that at all the centres, the likely commencement of southwest monsoon would be in the 11th fortnight. Suitable probability distributions from among normal, root normal, log normal and gamma distribution were selected and fitted to fortnightly amounts of rainfall. Rainfall probabilities of getting a fixed amount or less of rainfall wore worked out together with the 80% and 90% confidence limits of the mean fortnightly rainfall. The 3rd fortnight of the year all over the centres was found to be the driest fortnight and the 12th or 13th fortnight was found to be the wettest fortnight of the year.ThesisItem Open Access Standardisation of techniques of clustering genotypes using mahalanobis D2 and wilks ^ criterion(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1986) Suresh, K M; KAU; Gopinathan Unnithan, V KTwo major drawbacks of Tocher's method of clustering genotypes using Mahalanobls D were pointed out and animprovement over Tocher's method was suggested. The cluster configuration obtained by these two methods were compared with those obtained by canonical analysis method. A new computer oriented iterative algorithm for clustering using Mahalanobis D values was proposed. A procedure for formation of clusters statistically, using O V Mahalanobls Er was suggested to form maximum nonsignificant subsets of genotypes. A new measure of dissimilarity which does not require any assumption on distribution of the population, viz., the determinant of the pairwise scatter matrix was proposed in the study. Minimum /W/ criterion of Friedman and Rubin (1967) was also used for clustering. The clustering obtained by the new iterative algorithm using either Mahalanobls or determinant of pairwise scatter matrix or both could be used as the initial solution for it A graphical method for determining the optimum number of clusters was suggested The different methods were illustrated in two sets of dataThesisItem Open Access Optimum size of plots in cocoa (Theobroma cacoa L.) a multivariate case(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1987) Sheela, M A; KAU; Gopinathan Unnithan, V KA procedure to determine optimum size of experimental units in the multivariate case was proposed. For the purpose, the matrix of relative dispersion was defined and its determinant was used as the measure of variation for comparison of plots of different sizes. This procedure was illustrated with the help of observations on three characters of 738 trees of 'Forastero1 variety of cocoa raised in the' KADP farm of the Kerala Agricultural University, Vellanikkara. Optimum plot size also was obtained in the univariate case. The following three different methods of plot formation were used in this investigation. Method I The whole set of trees were divided into compact blocks of different sizes and plots of one to fifteen trees were formed by combining adjacent trees in the field. Method II All trees were arranged in descending order of magnitude of trunk girth and of the canopy spread separately and were divided into blocks of required size. Plots of one to fifteen trees were formed by combining adjacent trees in the list in each block for each arrangement. Method III The trees were first arranged in descending order of magnitude of each character and they were divided into blocks of required size. Plots of different sizes were formed within each block by the following procedure, let there be 'nk* trees in a block. The nk trees were divided into 1 n 1 groups of 'It* trees each bearing continuous serial numbers * When 'n' is even, the 1st plot was formed by combining 1th tree from each of the first 'n/2* groups and (k-i+j)st tree from each of the remaining 'n/2' groups, where i=1,2,....n. When 'n1 is odd, ith plot was formed by combining the i^h tree from each of the first (J[n+iy2) groups and (k-i+fy9^ tree from each of the remaining [(n-lj/2) groups, whore 1=1,2, n. Of the three methods of plot formation Method III, which was proposed in this study was found to be superior to Methods I and II for experiments in established gardens and Method I for experiments for which fresh planting is required Optimum size of plots were al so determined by three different methods viz., (a) that which requires minimum experimental material for a specified precision (b) that which has maximum efficiency and (c) that for which the best fitting model has maximum curvature.ThesisItem Open Access Standardization of field plot technique for cashew(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1986) Lucyamma Mathew; KAU; Saraswathi, PThe present study deals with a plot technique for conducting field experiments on a biologically heterogeneous tree crop cashew by applying a well known result in sampling theory that the clusters formed with negative intraclass correlation are relatively more efficient Cashew being a perennial crop are sensitive to variation in fertility status of soil in which they grow, susceptable to mishaps, long gestation period etc Because of their large size and long life they are considerably different from annuals or field crops as to need special considerations in designing experiments with them. The experimenter is always faced with the dlffiiculty of getting uniform experimental trees on account of the biological variation present among the individual trees. The difficulty in getting experimental trees with uniform yield or some other measurable characteristic of the tree and some considerations in overcoming this problem is discussed. Achieving greater homogeneity between plots within a block by creating greater heterogeneity within plots is found to be a better field plot technique for experiments with adult trees on cashew. Similar techniques are also applicable to other plantation crops which are subjected to high biological variation.ThesisItem Open Access Comparative study of growth pattern in ducks - a practical approach(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1989) Vishnu Namboodiri, M; KAU; George, K CAn investigation based on 14 Desi males, 25 Desi females, 26 White Pepkin (WP) males and 26 WP females belonged to the Kerala Agricultural University Duck Farm, Mannuthy was undertaken (i) to examine the pattern of growth in the two breeds of ducks (ii) to compare the rates of growth between and within each genetic groups and (iii) to fit appropriate growth curves for prediction of body weight at different stages of growth. The ducklings were reared under uniform feed formula and identical management practices. The initial mean body weights of the six groups of ducklings viz. Desi males, Desi females,WP males, WP females, Desi ducklings irrespective of sex and WP ducklings irrespective of sex were 36.6428 g, 38.16 g, 38.6538 g, 38.3486 g, 37.6153 g and 38.4423 g respectively. Females in each genetic groups had a higher mean body weight than males except 11th and 12th week in the case of Desi ducklings. On the 12th week the body weight averaged 1291.7857 g, 1239.4 g, 1021.7308 g, 1401.6154 g, 1258.2051 g and 1214 g for Desi males, Desi females, WP males, WP females, Desi ducklings irrespective of sex and WP ducklings irrespective of sex respectively. The initial body weight was non significant for all the four groups whereas the 4th, 8th and 12th week body weights showed significant difference between groups. It could be observed that a plateau in body weight was not attained on the 12th week of age for Desi and white pepkin ducklings. Gompertz (y = abcx), modified exponential (y = k+abx) and Von-Bertalanffy (yt = A(1-be-kt)3 were found suitable for fitting body weights for the first 12 weeks. The first two gave good fit to almost all birds on individual and average basis. When the growth rates of the fitted curves were compared, Gompertz curve showed significant difference between groups. The maximum growth rate was noticed inDesi females. Based on modified exponential and Von-Bertalanffy the rate of growth was significant and maximum growth was noticed for WP males. By the method of Rao (1958) the initial body weight had significant relation with the growth rate (b). The rate of growth was maximum for WP females followed by Desi females. The graphs of the best fitted curves – Gompertz, modified exponential and Von-Bertalanffy were drawn for all the six groups along with the observed values and that also confirms the above findings.