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Sher-e-Kashmir University of Agricultural Sciences and Technology, Jammu
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ThesisItem Open Access Some New Aspects of Post stratification in Sample Surveys(Sher-e-Kashmir University of Agricultural Sciences & Technology of Jammu, 2024-05-09) Shah, Mohd Younis; Rizvi, S.E.H.Post-stratification, also known as stratification after sample selection is a sampling method employed when there's a desire to categorize based on an important variable, yet it's not feasible to assign units to their respective groups until after the sample is chosen. The resulting weights are then used in forming estimates of means or totals of variables collected in the survey. Inferences can be made either unconditionally, i.e. across all possible realizations of the post-strata sample sizes, or conditionally given the achieved sample sizes. The present study “Some New Aspects of Post stratification in Sample Surveys” has been undertaken with objectives to develop some improved estimators of variance for conditional as well as for unconditional post stratification and improved post stratified estimators of mean in two stage sampling design by using auxiliary information. The expressions for bias and mean square error (MSE) of proposed estimators have been obtained up to the first order of approximation. The theoretical results are supported by numerical data that demonstrate the efficiency of the proposed estimators over existing estimators in terms of mean square error. For objective first, (the study variable (Y) and the auxiliary variable (X)), the improved exponential product type estimatorσ ̂_pst(t1)^2 has been proposed. For objective second, (the study variable (Y) and the auxiliary variable (X)), the improved combined estimator for estimating the finite population variance σ ̂_pst(t2)^2 has been proposed and for objective third, (the study variable (Y) and the auxiliary variable (X)), the post-stratified separate ratio type exponentialestimator in two stage sampling designY ̅_TS has been proposed. Based on percent relative efficiency, all the proposed estimators(σ ̂_pst(t1)^2=191.76, σ ̂_pst(t2)^2 = 586.05 and Y ̅_TS = 8170.43) are found to be more efficient than Sadia and Masood (2015) and other existing estimators like Yadav et al. (2018) and other authors in respective cases.ThesisItem Open Access Evaluating XAI for Weed Localization in Crop Images: Survey Based Hypothesis Testing(Sher-e-Kashmir University of Agricultural Sciences & Technology of Jammu, 2024-04-18) Mahajan, Sukanya; Rizvi, S.E.H.Weeds are considered as undesirable vegetation that competes with cultivated plants for essential resources such as light, water, and nutrients. This competition can lead to a decrease in the yield and quality of the desired crops. When examining the potential agricultural losses caused by various factors, it is evident that weeds are the most significant, accounting for approximately 34 percent of the potential loss. In comparison, animal pests and pathogens are of lesser concern, contributing to losses of 18per cent and 16per cent respectively. The impact of weeds on agricultural production is substantial, with an estimated average loss of 5 percent in developed countries, 10 percent in developing countries, and a significant 25 percent in the least developed countries.Weed management involves the elimination of weeds and control its growth through micro-spray, cutting, thermal, electrocution, automated weeding system etc. Presently, weed management and control is executed using mostly herbicides.However, the extensive usage of herbicide causes harm to the environment, raises concern about risks to human health and is expensive.To address these challenges, the present investigation entitled “Evaluating XAI for Weed Localization in Crop Images: Survey Based Hypothesis Testing” have been focused on building an automated weeding solution in the research with the objectives to encompass the development of a binary classifier, generating visual explanation for the results predicted by the classifier and finally evaluating these visual explanationsthrough hypothesis testing. To conduct this study cotton (Gossypium sp.) crop and weeds image dataset was taken from Kaggle. Then“TinyVGG” model was trained, validated and tested on a customized image dataset. Evaluation of this model overtest set resulted in an accuracy of 95.52per cent. F1 score of the model was 95.46per cent. Then, two techniques of Explainable Artificial Intelligence (XAI) i.e. local interpretable model-agnostic explanations (LIME) and gradient-weighted class activation mapping (Grad-CAM) to generate visual explanations on the output predicted by the classifier were adopted. Further,a survey was created with the aim of evaluating these visual explanations by humans, called human-centric evaluations which refers to assessments conducted based on human criteria, evaluating how explanations align with human perceptions and whether they fulfill human needs or not, using hypothesis testing.Based on human-centric evaluation, a significant difference between LIME explanations and Grad-CAM explanations was discovered. And, finally Grad-CAM technique resulted in superior performance when presented to participants.ThesisItem Open Access MODIFIED RATIO AND PRODUCT TYPE ESTIMATORS UNDER ADAPTIVE CLUSTER SAMPLING(Sher-e-Kashmir University of Agricultural Sciences & Technology of Jammu, 2023-10-27) Bhat, Arshid Ahmad; Sharma, Manish Kr.In sample surveys there are the cases when the population is rare and clustered. The sampling method used to obtain the sample in these cases is known as Adaptive Cluster Sampling. Adaptive cluster sampling (ACS) refers to the design in which an initial unit is selected by probability sampling procedure namely Simple Random Sampling without replacement and whenever the variable of interest of a selected unit satisfies a given pre-defined condition, additional units in the neighborhood of that unit are added to form the sample. The present investigation entitled “Modified Ratio and Product Type Estimators under Adaptive Cluster Sampling” has been undertaken with the objectives to develop some generalized ratio and product type estimators for estimating the population mean under ACS. The additional information used in order to improve the efficiency of the ratio and product type estimators is known as auxiliary information. The large sample property of mean square error (MSE) for the proposed estimators have been derived up to first order of approximation and are compared with the conventional and existing estimators both theoretically as well as empirically. The generalized class of ratio type estimators (t_(p,q)^ri) under ACS has been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, p,q where i = 1, 2, 3, 4, p and q are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinations of i, p and q are found efficient than the existing estimators taken in the literature. Among the developed cases the different values of p and q have been determined and the estimators namely 〖 t〗_2,2^r1,t_5,10^r2,t_8,9^r3 and t_2,2^r4 are found most efficient theoretically and empirically than the existing estimators as proposed by Cochran (1940), Sisodia and Dwivedi (1981), Upadhyay and Singh (1999), Singh and Tailor (2003), Kadilar and Cingi (2003), Dryver and Chao (2007), Yan and Tian (2010), Chutiman (2013), Yadav et al. (2016). The generalized class of product type estimators (t_(k,k')^pi), (t^p4) and (t_(k,k')^p5) under ACS have also been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, k, k ' where i = 1, 2, 3,k and k ' are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinatioIn sample surveys there are the cases when the population is rare and clustered. The sampling method used to obtain the sample in these cases is known as Adaptive Cluster Sampling. Adaptive cluster sampling (ACS) refers to the design in which an initial unit is selected by probability sampling procedure namely Simple Random Sampling without replacement and whenever the variable of interest of a selected unit satisfies a given pre-defined condition, additional units in the neighborhood of that unit are added to form the sample. The present investigation entitled “Modified Ratio and Product Type Estimators under Adaptive Cluster Sampling” has been undertaken with the objectives to develop some generalized ratio and product type estimators for estimating the population mean under ACS. The additional information used in order to improve the efficiency of the ratio and product type estimators is known as auxiliary information. The large sample property of mean square error (MSE) for the proposed estimators have been derived up to first order of approximation and are compared with the conventional and existing estimators both theoretically as well as empirically. The generalized class of ratio type estimators (t_(p,q)^ri) under ACS has been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, p,q where i = 1, 2, 3, 4, p and q are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinations of i, p and q are found efficient than the existing estimators taken in the literature. Among the developed cases the different values of p and q have been determined and the estimators namely 〖 t〗_2,2^r1,t_5,10^r2,t_8,9^r3 and t_2,2^r4 are found most efficient theoretically and empirically than the existing estimators as proposed by Cochran (1940), Sisodia and Dwivedi (1981), Upadhyay and Singh (1999), Singh and Tailor (2003), Kadilar and Cingi (2003), Dryver and Chao (2007), Yan and Tian (2010), Chutiman (2013), Yadav et al. (2016). The generalized class of product type estimators (t_(k,k')^pi), (t^p4) and (t_(k,k')^p5) under ACS have also been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, k, k ' where i = 1, 2, 3,k and k ' are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinations of i, k and k' are found efficient than the existing estimators. Among the developed cases the proposed values of k and k ' have been determined from those estimators and the estimators namely〖 t〗_4,8^p1,〖 t〗_(-1,-2)^p2,t_(-1,-2)^p3, t^p4 , t_(1,-1)^p5 and are found the most efficient theoretically and empirically than the estimators proposed by Robson (1957), Bahl and Tuteja (1991), Shahzad and Hanif (2016), Panda and Samantary (2018) and Hussain et al. (2021). Thus the proposed generalized ratio and product type estimators under ACS are superior over existing estimators theoretically as well as empirically. ns of i, k and k' are found efficient than the existing estimators. Among the developed cases the proposed values of k and k ' have been determined from those estimators and the estimators namely〖 t〗_4,8^p1,〖 t〗_(-1,-2)^p2,t_(-1,-2)^p3, t^p4 , t_(1,-1)^p5 and are found the most efficient theoretically and empirically than the estimators proposed by Robson (1957), Bahl and Tuteja (1991), Shahzad and Hanif (2016), Panda and Samantary (2018) and Hussain et al. (2021). Thus the proposed generalized ratio and product type estimators under ACS are superior over existing estimators theoretically as well as empirically.ThesisItem Open Access Scenario and Statistical Modeling of Oilseed Production for Jammu and Kashmir(Sher-e-Kashmir University of Agricultural Sciences & Technology of Jammu, 2023-10-25) Singh, ChibPrerna Ran; Rizvi, S.E.H.It is well known that India has 20.8% of the total area globally under oilseeds and accounts for 10% of global production having fourth largest position and hence oilseeds occupy an important position in the country’s economyin terms of area and production. As a result, it is critical to have an idea of future production and productivity. Thus, the present investigation entitled “Scenario and Modeling of Oilseeds Production for Jammu and Kashmir” has beenconducted with the objectives to study the aspects relating to behaviour of time series data on production and productivity of oilseeds crops, selection of an appropriate model, it’s fitting, testing and forecasting future values using time series modelling and Artificial Neural Network (ANN) models. For this purpose, secondary data were obtained for UT of Jammu & Kashmir as well at national level for the period of 1984 to 2022. Then the data were analysedfor obtaining the trend for the period using models like linear, quadratic, cubic, exponential, compound, power etc.Descriptive statistics wereobtained on entire data as well as on decadal basis to have information scenario of oilseeds production.The best models were chosen based on minimum Root Mean Square Error (RMSE).Time series models were obtained for oilseedsproduction and productivity at national as well as Jammu and Kashmir levels. Based on minimum RMSE, at national level the Logarithmic model for area, Linear model for production as well as productivity were found to be of best fit. Similarly, at Jammu and Kashmir level for area, productionand productivity,Cubic, Cubic and Quadratic models, respectively, were found to be of best fit.Instability index for area, production, and productivity of oilseeds at national level and at Jammu & Kashmir level indicated that instability in area, production, and productivity of oilseeds in India were of low level whereas in UT of Jammu and Kashmir it was of medium level. Growthmodels such asGompertz model, Monomolecular and Sigmoid were fitted for National and Jammu & Kashmir levels so as to observe growth in oilseeds production. Based on exponential model, overall percentage compound growth rates for area in Jammu and Kashmir during study period was negative (-0.12%) wheras as at national level it was 7.02%. For production atJammu and Kashmir levelit showedgradual growth with 0.08% and somewhat satisfactory in case of productivity with 1.01% CGR value.For production at all India level it showed remarkable growth with 2.53% and better in case of productivity with 1.81% CGR value.Using RStudio Estimated parameters for National of Gompertz, S-curve.This indicates increasing growth pattern over the timeseries ARIMAmodel best suited for production are ARIMA (2,0,1) forUT of Jammu and Kashmir level. For Artificial Neural network (ANN), the data were normalised and then the normalised data were further divided into two parts train data and test data. For the accuracy, data here were divided into (80:20) where 80% is train data sand 20% is test data, its MSE value is 0.16. Comparative to ANN, time series model is found to be the best fit.ThesisItem Open Access Some Improved Ratio and Regression Type Estimators in Case of Non-Response(Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, 2022-11) Wani, Zakir Hussain; Rizvi, S.E.H.In sample surveysgenerallyit is not possible that sample will represent population truly, which results in two types of errors viz. (i) sampling error, and (ii) non-sampling error.Non-response is a type ofnon-sampling error. The present investigation entitled“Some Improved Ratio and Regression Type Estimators in case of Non-Response” has been undertaken with the objectives to develop some improved types of separateand combined ratio as well asregression estimatorsfor estimating the population mean in presence of non-response, using auxiliary information, for four cases. The expressions for bias and mean square error (MSE) of proposed estimatorshave been derived up to first order of approximation. Theoretical comparisons of proposed estimators with the usual unbiased estimator by Hansen and Hurwitz (1946) and other existing estimators have been made. The theoretical results are supported by numerical data that demonstrate the superiority of the proposed estimators over existing estimators in terms of mean square errors. For Case I (non-response occurs on both the study variable (Y) and the auxiliary variable (X), and the population mean X ̅ is known) the separate andcombinedratio estimators t_1^(*(i))andt_2^(*(i)),i=1 to 10,respectively,separate and combined regression estimatorst_3^(*(i)) andt_4^(*(i)),i=1 to 5,respectively,have been proposed. ForCase II (non-response occurs on Y only, information on X is obtained from all the sample units and X ̅ is known) the separate and combined ratio estimatorst_1^('(i)) and t_2^('(i)),i=1 to 10, respectively,separate and combined regression estimatorst_3^('(i)) andt_4^('(i)),i=1 to 5,respectively,have been proposed. For Case III (non-response occurs on both Y and X, but X ̅ is unknown) the separate and combined ratio estimatorst_5^* andt_6^*, separate and combined regression estimatorst_7^(*(i)) andt_8^(*(i)),i=1 to 12, respectively,have been proposed.For Case IV(non-response occurs on Y, information on X is obtained from all the sample units, but the Mean X ̅ is unknown) the separate and combined ratio estimators t_5^'andt_6^', separate and combined regression estimatorst_7^('(i)) and t_8^('(i)),i=1 to 12,respectively, have been proposed. Based on percent relative efficiency, all the proposed estimators are found to be more efficient than the Hansen and Hurwitz (1946) and other existing estimators like, classical separate and combined ratio as well as regression estimators, estimators proposed by Onyekaet al. (2019)and other researchersin respective cases.ThesisItem Open Access Construction of Strata Boundaries under Ranked Set Sampling(Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, 2022-11) Rather, Khalid Ul Islam; Rizvi, S.E.H.The principal reason for stratification in the design of sample surveys is to reduce the sample variance of the estimates, so as to gain a higher degree of relative precision. The problem of determining optimum strata boundaries (OSB) on the basis of study variable was pioneered by Dalenius (1950), who treated study variable itself as stratification variable and used an approach which provided exact solution. Researchers like Dalenius and Gurney (1951), Singh (1971), considered the problem of optimum stratification using auxiliary variable as stratification variable, since the probability density function of the study variable is in general unknown prior to study. In these studies simple random sampling was considered as method of selection of sampling units in individual strata. It is well known that ranked set sampling (RSS) introduced by McIntyre (1952) provides an increased precision as compared to simple random sampling. Thus, the RSS method if used for selection of sampling units in individual strata, the relative efficiency is expected to be increased. Therefore, the present investigation has been undertaken to deal with the problem of construction of strata when ranked set sampling is used. In this regard, various allocation procedures viz. proportional, optimum as well as equal allocations have been considered and accordingly the methods of construction of strata have been developed through minimization of variance under ranked set sampling. The method of selecting the best boundaries that makes strata within them self-homogeneous as far as possible is known as optimum stratification. If the frequency distribution of the study variable is known, the stratification points could be obtained by cutting the range of the distribution. And, if unknown the points of stratification may be approximated on the basis of auxiliary variable. In the present study, theories have been developed for optimum stratification using one auxiliary variable as stratification variable. Minimal equations giving approximate optimum strata boundaries (AOSB) have been obtained for stratified ranked set sampling (SRSS) under different methods of allocations, by minimizing the variance of the sample estimates. For these cases, rule and rule , where the function takes different forms for different allocations, have been developed. Under the classical optimization technique the empirical studies on uniform, right triangular, exponential and normal distribution have been made which resulted gain in efficiency. On comparison of the efficiency, it has been observed that the proposed methods for SRSS under various methods of allocations performed better than unstratified RSS.ThesisItem Open Access Comparative Study of Ranked Set Sampling Methods under Skewed and Unskewed Distributions(Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, 2022-10) Rashid, Imran; Jeelani Bhat, M. IqbalRanked set sampling (RSS) isa special cost-effective sampling method used in situations where judgment of units can be done easily without any difficulty. The estimates based on RSS are more efficient in comparison to the traditional unrestricted sampling procedures and in recent past its modified versions have come into prominence due to their remarkable gain in efficiency inforest management research works. Inview of this the present study entitled “COMPARATIVE STUDY OF RANKED SET SAMPLING METHODS UNDER SKEWED AND UNSKEWED DISTRIBUTIONS”was carried out on skewed and unskewed distributions to evaluate the different modified versions of RSS in terms of efficiency. In order to achieve stipulated objectives simulated data wasgenerated in RStudio(version 4.1.2 -2021) utilizing Skewed and Unskewed probability distributions like gamma, exponential, uniform and normal distribution.Accordingly a ranked set sample of size150, 300, 450, 600, 750, 900, 1050, 1200 with a set size of 3,6,9,12,15,18,21,24utilizing a constant cycle (r) 50 respectively were drawn from the simulated data through different modified methods of RSS like : Extreme ranked set sampling (ERSS), Median ranked set sampling (MRSS), Percentile rank set sampling (PRSS), Balanced grouped ranked set sampling (BGRSS), Double rank set sampling (DRSS) and Truncation based rank set sampling (TBRSS)by means oflibrary( RSSampling) of R Studio. From the results it was observed that modified versions of RSS performed better in unskewed distributions in comparison to skewed distribution in terms of efficiency, asthese samples are based on modified versions of RSS which are more regularly spaced and induces stratification at sample level which involves the gain in efficiency. Also, from this study it was found thatefficiency of allmodified RSS methods increases as the sample size increases.Based on empirical investigation through simulated data, it was observed that across the modified RSS methods, Truncation based rank set sampling (TBRSS) performed better in comparison to its counterparts in terms of efficiency.Goodness of fit results revealed that the value of AIC & BIC decreased as the set size across the modified RSS methods increases, indicating that less amount of information is lostas set size increases. Finally, it is concluded that RSS has itspractical implications, where R packages facilitates a lot in implementation of modified RSS methods which are very informative and applicable to sample surveys.ThesisItem Open Access Statistical Model for the Estimation and Projection of Agriculture Share in India’s Gross Domestic Product(Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, 2022-10) Sharma, Arayan; Sharma, Manish Kr.An investigation titled “Statistical Models for the Estimation and Projection of Agriculture Share in India’s Gross Domestic Product” was conducted with the objectives: To analyse the Gross Domestic Product of India through time series models and to assess statistically the estimation and projection of agricultural components in Gross Domestic Product. India is an agricultural-based economy with more than 52.6 percent of land area that is considered arable. The Gross Domestic Product (GDP) of Agriculture and allied sectors has been declining since 1991 and is at 18.8 per cent in the present scenario. The secondary data of the GDP has been used for this study. The data on time series pertains to GDP and individual GDP components that are Agriculture, Livestock, Food processing industries, and Forestry, been collected from different reports published by different Government Offices like Economic Survey, NitiAayog Report, Food and Agriculture Organization Report and MOSPI. The estimation and projection of models have been done by using the techniques through ARIMA, Baysian, Correlation, Regression, and Stepwise regression. The results of the studyrevealed a huge fluctuation in the economy in the past two decades within the last seven decades. The ADF test for the stationarity of the data was tested which failed so to handle the problem differences 1,2 and 3 were applied. The 2nd degree of differences was selected as it showed the least deviation and was significant (ADF test) for the time series model. The best-proposed model was ARIMA (1,2,1). The forecasted value of GDP for 2029-30 is ₹376.07 lakh crores with a lower CL (0.95) value of ₹326.14 lakh crores and upper CL (0.95) value of ₹426.01 lakh crore. Similarly, the forecasted values of GDP for 2039-40 and 2046-47 are ₹543.71 lakh crores and ₹686.87 lakh crores with a lower CL (0.95) value of Rs.428.51 lakh crores and ₹509.81 lakh crores and upper CL (0.95) value of Rs.658.92 lakh crores and Rs.863.92 lakh crores respectively. Further, the data pertains to GDP (Endogenous) and Agriculture, FPI, Food processing and Livestock (Exogenous) were found to be reliable and Normal. The main component significantly were Agriculture and FPI for enhancing the FPI sector for boosting the Indian GDP in addition to this Bayesian estimation the maximum posterior probability for increasing the GDP will be through agriculture and FPI. As per the assessment of GDP, the interaction between Agriculture with Forestry, FPI and Livestock are 70.08 perc ent, 67.66 per cent and 65.25 per cent respectively. In the coming years, FPI and Forestry will contribute more to the GDP as compared to LivestockThesisItem Open Access ARIMA Modeling for Maize Production and Productivity in Jammu Division(Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, 2022-09) Tahir, Mohd; Rizvi, S.E.H.An investigation was conducted with the objectives to assess the production and productivity of maize on decadal basis along with instability index as well as to fit ARIMA model (s) for production and productivity of maize in Jammu division. It is known that maize is one of the world's most important cereal crops which it helps to ensure food security in the majority of developing countries. Maize is emerging as India's third most important crop after rice and wheat. As a result, it is critical to have an idea of future production and productivity. For this purpose, secondary data were obtained from the Directorate of Agriculture, Jammu for the period 1990 to 2019. The data were analyzed for obtaining the trend on a decadal basis and for entire period using ten known models such as the linear, quadratic, cubic, exponential etc. were fitted. The statistically best models were chosen based on adjusted R2 and co-efficient of determination (R2) and an instability index has been calculated. On the basis of time series data set of the study period, the overall average production under maize in Jammu division was 403.327 MT and overall average productivity was 18.72 q/ha. Different time series models were obtained for production as well as productivity of maize for Jammu division. On the basis of R2 and adj. R2, the cubic model for production as Ŷ=299.496+28.993t-2.178t2+0.047t3 was found to be best fitted (p-value<.023) and for productivity also cubic model obtained as Ŷ=12.634+1.829t-1.44t2+0.003t3 was found to be best fitted (p-value < .001) for overall Jammu division. The instability index for production was obtained as 11.371 and for productivity it was 8.744. Further using R-Software the data has been analyzed for the ARIMA model. An autoregressive integrated moving average (ARIMA) is a type of regression analysis that shows how strong a dependent variable is in comparison to other changing variables. The model's ultimate goal is to predict future time series movement by examining differences between values in the series rather than actual values. ARIMA models are used when there is evidence of non-stationarity in the data. Non-stationary data are always transformed into stationary data in time series analysis. Different ARIMA model combinations were created, and appropriate ARIMA models were fitted after the data was judged for stationarity. The statistically appropriate model was chosen based on goodness of fit criteria, including Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC), RMSE, MAE assumptions of normality and residual independence. The best fitted model ARIMA (1, 3, 2) for the production and ARIMA (2, 2, 1) for productivity of maize crop in Jammu division. Based on these models, maize production and productivity have been forecasted for the five year from 2020-2024 with the values for production are 532.86, 573.41, 601.12, 642.52, 687.70 MT and for productivity the forecasted values are 27.05, 29.19, 31.72, 32.88 and 34.71q/ha, respectively.
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