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2016 - 20172
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Subject: Biostatistics × Thesis Type: Ph.D ×
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    ThesisItemOpen Access
    SOME CONTRIBUTIONS IN THE THEORY OF CONSTRUCTION OF STRATA
    (UHF,NAUNI, 2016) THAKUR, ASHU; MAHAJAN, P.K.
    ABSTRACT The method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation, is known as optimum stratification. To achieve this, the strata are constructed in such a way that the strata variances should be as small as possible for the characteristic under study. Present study considers the problem of finding optimum strata boundaries to optimize the estimation of sensitive/stigmatized characters when sample sizes from different strata are selected with simple random sampling with replacement (SRSWR) and probability proportional to size sampling with replacement (PPSWR) and the data are collected by scrambled randomized response technique on the sensitive study variable. Assuming the form of the regression of the estimation variable y on the auxiliary variable x as y = ƞ(x) + e and the form of the conditional variance V (Y/X), the minimal equations giving optimum strata boundaries by minimizing the variance of the estimator of the population mean have been obtained. Due to implicit nature of these equations, the approximate solutions to these minimal equations have been found to give approximate optimum strata boundaries (AOSB). The total four rules have been proposed to have AOSB i.e. for Neyman allocation with SRSWR, equal and proportional allocation in PPSWR and for ratio and regression method of estimation. Limiting expressions for the variance of the estimator of population mean have also been suggested. Numerical investigation into the relative efficiency of stratification under all considered allocations with respect to no stratification have also been made for three usually encountered distributions namely rectangular, right triangular and exponential.
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    ThesisItemOpen Access
    “Statistical investigations on kinnow mandarin (Citrus reticulate Blenco.) production in Himachal Pradesh”,
    (UHF,NAUNI,SOLAN, 2017) VERMA, GEETA; MAHAJAN, P.K.
    ABSTRACT The study was carried out in Kangra and Sirmour districts of Himachal Pradesh with special reference to comparison of different sample allocation methods in combination with various stratification rules for determination of optimum strata boundaries. For this purpose, four methods of construction of strata boundaries viz., equalization of strata total, equalization of cum. , equalization of cum. {r(y)+f(y)} and equalization of cum. rules were used and it was observed that variance term worked out to be least in Neyman allocation and hence this allocation method was retained for further investigation. The critical examining of the results also revealed that for varying sample size, equalization of cum. provided the least variance, therefore, the study inferred that sampling methodology for estimation, “Statistical investigations on kinnow Mandarin (Citrus reticulata Blenco.) production in Himachal Pradesh” should be in conjunction with cum. can be used for estimation of kinnow production. To assess the relative contribution of various morphological characters in increasing the kinnow yield, 104 trees from location-1 and 96 trees from location -2 were randomly selected in the year 2014-15. F-test suggested that there was significant variation among all the characters between these two locations except fruit weight and LD ratio. It was also observed that number of flowers per branch, number of fruits per branch, plant girth and fruit weight contributes significantly towards the kinnow yield. In relation to the socio- economic status of kinnow orchardists, it was observed that the contribution of fruit crops towards the gross farm income had shown an increasing trend, while the contribution of field crops had shown a declining trend with the increase in farm size. At overall level, fruits crop accounted for 62.68 percent while field crops accounted only 37.32 percent of the total gross farm income. In relation to the price spread of kinnow under different marketing channels in the Himachal Pradesh indicated that producers’ share in consumers’ rupee was highest in channel-IV (81%), followed by channel-III (51%) and channel-I (43%), therefore, the marketing efficiency was found maximum (4.35) when farmers sold their produce directly to consumers.