This study investigates the process for estimating the mean number of individuals having rare sen... more This study investigates the process for estimating the mean number of individuals having rare sensitive attribute in stratified random sampling for known population using Poisson distribution. The properties of the suggested estimation procedures are deeply examined. Empirical studies are performed to support the theoretical results, which show the dominance of the proposed estimators over well-known existing estimators. The results are interpreted and suitable recommendations have been put forward to the survey practitioners.
Journal of Applied Mathematics, Statistics and Informatics
In this study, the difficulty of estimating the population mean in the situation of post-stratifi... more In this study, the difficulty of estimating the population mean in the situation of post-stratification is discussed. The case of post-stratification is presented for ratio-type exponential estimators of finite population mean. Mean-squared error of the proposed estimator is obtained up to the first degree of approximation. In the instance of post-stratification, the proposed estimator was compared with the existing estimators. An empirical study by using some real data and further, simulation study has been carried out to demonstrate the performance of the proposed estimator.
Background: In this study 11 height and diameter prediction models were fitted and evaluated for ... more Background: In this study 11 height and diameter prediction models were fitted and evaluated for Himalayan Chir pine (Pinus roxburghii) in Jammu region of UT J and K (India). The data were collected from 50 permanent sample plots in uneven aged stands of Pinus roxburghii and total of 500 individual tree height and diameter measurement were used for this study. At initial stage all the models fitted resulted in significant coefficients, besides various selection criteria's were also used to test the predictive performance of fitted models. The results of these criteria were generated from various libraries of R studio (version 3.5.1, 2018). The models were further cross validated and results revealed Manfred (MG) and Michaelis-Menten2 (MJ) models described the highest amount of height variation in terms of fit statistics and more crucially with lowest prediction error rate as compared to other models. Methods: The study was carried out in Jammu region of UT J and K (India). Data used in this study were collected on 50 permanent sample plots of 0.25 ha in size. In order to achieve stipulated objectives, Height diameter data on 500 trees from Jammu forest division was utilized in this study. Result: The summary statistics of height and diameter variable and the overall summary of the coefficients of various height and diameter models in Jammu forest division are presented. Almost all the coefficients of the statistical models were statistically significant which is an indication that fitted models are capturing the height diameter relationship an important aspect in context to biological realism.
In this article, a new robust ratio type estimator using the Uk’s redescending M-estimator is pro... more In this article, a new robust ratio type estimator using the Uk’s redescending M-estimator is proposed for the estimation of the finite population mean in the simple random sampling (SRS) when there are outliers in the dataset. The mean square error (MSE) equation of the proposed estimator is obtained using the first order of approximation and it has been compared with the traditional ratio-type estimators in the literature, robust regression estimators, and other existing redescending M-estimators. A real-life data and simulation study are used to justify the efficiency of the proposed estimators. It has been shown that the proposed estimator is more efficient than other estimators in the literature on both simulation and real data studies.
Pakistan Journal of Statistics and Operation Research
In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the expo... more In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the exponential function for the population mean in case of non-response for simple random sampling for the estimation of the mean of the population with the RSS (ranked set sampling) method. The equations for the MSE and the bias of the adapted estimators are obtained for RSS and it in theory shows that the proposed estimator is additional efficient than the present RSS mean estimators in the literature. In addition, we support these theoretical results with real COVID-19 real data and conjointly the simulation studies with different distributions and parameters. As a result of the study, it was observed that the efficiency of the proposed estimator was better than the other estimators.
Background: In this study 11 height and diameter prediction models were fitted and evaluated for ... more Background: In this study 11 height and diameter prediction models were fitted and evaluated for Himalayan Chir pine (Pinus roxburghii) in Jammu region of UT J and K (India). The data were collected from 50 permanent sample plots in uneven aged stands of Pinus roxburghii and total of 500 individual tree height and diameter measurement were used for this study. At initial stage all the models fitted resulted in significant coefficients, besides various selection criteria’s were also used to test the predictive performance of fitted models. The results of these criteria were generated from various libraries of R studio (version 3.5.1, 2018). The models were further cross validated and results revealed Manfred (MG) and Michaelis-Menten2 (MJ) models described the highest amount of height variation in terms of fit statistics and more crucially with lowest prediction error rate as compared to other models. Methods: The study was carried out in Jammu region of UT J and K (India). Data used...
Optimum stratification is the method of choosing the best boundaries that make strata internally ... more Optimum stratification is the method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation. In order to make the strata internally homogenous, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. This could be achieved effectively by having the distribution of the study variable known and create strata by cutting the range of the distribution at suitable points. If the frequency distribution of the study variable is unknown, it may be approximated from the past experience or some prior knowledge (auxiliary information) obtained at a recent study. In this study, problem of optimum stratification on the auxiliary variable x for equal allocation has been considered. A ( ) 3 cum K x rule of obtaining approximately optimum strata boundaries has been proposed under ranked set sampling. A numerical investigation with relative efficiency has also been made.
Rice blast caused by Magnaporthe oryzae B.C. Couch is one of the major diseases of rice in severa... more Rice blast caused by Magnaporthe oryzae B.C. Couch is one of the major diseases of rice in several rice ecosystems of both tropical and temperate regions. The disease results in heavy yield losses ranging from 35 to 50 per cent and in certain cases, losses were estimated to be as high as 100 per cent (Padmavathi et al., 2005). Although, neck blast is more destructive in terms of yield loss, leaf blast may cause severe damage before plants reach reproductive phase of growth (Seebold et al., 2004). Nitrogen is an essential nutrient that affects crop growth, yield and quality, required at early and mid tillering stages to maximise the panicle number and during reproductive stage to produce optimum spikelets panicle -1
In this chapter, the authors consider the problem of estimating the population means of two sensi... more In this chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.
There are situations in survey sampling where the study characters are sensitive. Due to the sens... more There are situations in survey sampling where the study characters are sensitive. Due to the sensitivity of characters, practitioners don’t get the actual response. Randomized response technique (RRT) models are developed to reduce the bias raised by an evasive response on the sensitive variable. The measurement error (ME) is usually always present in the surveys so we need to study the RRT models with ME. We propose an estimator to predict the population mean of a sensitive variable in the influence of ME. The properties of the proposed estimator are studied and comparisons are made with the existing estimators. At last, a simulation study is executed to illustrate the results numerically.
This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set ... more This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.
This study investigates the process for estimating the mean number of individuals having rare sen... more This study investigates the process for estimating the mean number of individuals having rare sensitive attribute in stratified random sampling for known population using Poisson distribution. The properties of the suggested estimation procedures are deeply examined. Empirical studies are performed to support the theoretical results, which show the dominance of the proposed estimators over well-known existing estimators. The results are interpreted and suitable recommendations have been put forward to the survey practitioners.
Journal of Applied Mathematics, Statistics and Informatics
In this study, the difficulty of estimating the population mean in the situation of post-stratifi... more In this study, the difficulty of estimating the population mean in the situation of post-stratification is discussed. The case of post-stratification is presented for ratio-type exponential estimators of finite population mean. Mean-squared error of the proposed estimator is obtained up to the first degree of approximation. In the instance of post-stratification, the proposed estimator was compared with the existing estimators. An empirical study by using some real data and further, simulation study has been carried out to demonstrate the performance of the proposed estimator.
Background: In this study 11 height and diameter prediction models were fitted and evaluated for ... more Background: In this study 11 height and diameter prediction models were fitted and evaluated for Himalayan Chir pine (Pinus roxburghii) in Jammu region of UT J and K (India). The data were collected from 50 permanent sample plots in uneven aged stands of Pinus roxburghii and total of 500 individual tree height and diameter measurement were used for this study. At initial stage all the models fitted resulted in significant coefficients, besides various selection criteria's were also used to test the predictive performance of fitted models. The results of these criteria were generated from various libraries of R studio (version 3.5.1, 2018). The models were further cross validated and results revealed Manfred (MG) and Michaelis-Menten2 (MJ) models described the highest amount of height variation in terms of fit statistics and more crucially with lowest prediction error rate as compared to other models. Methods: The study was carried out in Jammu region of UT J and K (India). Data used in this study were collected on 50 permanent sample plots of 0.25 ha in size. In order to achieve stipulated objectives, Height diameter data on 500 trees from Jammu forest division was utilized in this study. Result: The summary statistics of height and diameter variable and the overall summary of the coefficients of various height and diameter models in Jammu forest division are presented. Almost all the coefficients of the statistical models were statistically significant which is an indication that fitted models are capturing the height diameter relationship an important aspect in context to biological realism.
In this article, a new robust ratio type estimator using the Uk’s redescending M-estimator is pro... more In this article, a new robust ratio type estimator using the Uk’s redescending M-estimator is proposed for the estimation of the finite population mean in the simple random sampling (SRS) when there are outliers in the dataset. The mean square error (MSE) equation of the proposed estimator is obtained using the first order of approximation and it has been compared with the traditional ratio-type estimators in the literature, robust regression estimators, and other existing redescending M-estimators. A real-life data and simulation study are used to justify the efficiency of the proposed estimators. It has been shown that the proposed estimator is more efficient than other estimators in the literature on both simulation and real data studies.
Pakistan Journal of Statistics and Operation Research
In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the expo... more In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the exponential function for the population mean in case of non-response for simple random sampling for the estimation of the mean of the population with the RSS (ranked set sampling) method. The equations for the MSE and the bias of the adapted estimators are obtained for RSS and it in theory shows that the proposed estimator is additional efficient than the present RSS mean estimators in the literature. In addition, we support these theoretical results with real COVID-19 real data and conjointly the simulation studies with different distributions and parameters. As a result of the study, it was observed that the efficiency of the proposed estimator was better than the other estimators.
Background: In this study 11 height and diameter prediction models were fitted and evaluated for ... more Background: In this study 11 height and diameter prediction models were fitted and evaluated for Himalayan Chir pine (Pinus roxburghii) in Jammu region of UT J and K (India). The data were collected from 50 permanent sample plots in uneven aged stands of Pinus roxburghii and total of 500 individual tree height and diameter measurement were used for this study. At initial stage all the models fitted resulted in significant coefficients, besides various selection criteria’s were also used to test the predictive performance of fitted models. The results of these criteria were generated from various libraries of R studio (version 3.5.1, 2018). The models were further cross validated and results revealed Manfred (MG) and Michaelis-Menten2 (MJ) models described the highest amount of height variation in terms of fit statistics and more crucially with lowest prediction error rate as compared to other models. Methods: The study was carried out in Jammu region of UT J and K (India). Data used...
Optimum stratification is the method of choosing the best boundaries that make strata internally ... more Optimum stratification is the method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation. In order to make the strata internally homogenous, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. This could be achieved effectively by having the distribution of the study variable known and create strata by cutting the range of the distribution at suitable points. If the frequency distribution of the study variable is unknown, it may be approximated from the past experience or some prior knowledge (auxiliary information) obtained at a recent study. In this study, problem of optimum stratification on the auxiliary variable x for equal allocation has been considered. A ( ) 3 cum K x rule of obtaining approximately optimum strata boundaries has been proposed under ranked set sampling. A numerical investigation with relative efficiency has also been made.
Rice blast caused by Magnaporthe oryzae B.C. Couch is one of the major diseases of rice in severa... more Rice blast caused by Magnaporthe oryzae B.C. Couch is one of the major diseases of rice in several rice ecosystems of both tropical and temperate regions. The disease results in heavy yield losses ranging from 35 to 50 per cent and in certain cases, losses were estimated to be as high as 100 per cent (Padmavathi et al., 2005). Although, neck blast is more destructive in terms of yield loss, leaf blast may cause severe damage before plants reach reproductive phase of growth (Seebold et al., 2004). Nitrogen is an essential nutrient that affects crop growth, yield and quality, required at early and mid tillering stages to maximise the panicle number and during reproductive stage to produce optimum spikelets panicle -1
In this chapter, the authors consider the problem of estimating the population means of two sensi... more In this chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.
There are situations in survey sampling where the study characters are sensitive. Due to the sens... more There are situations in survey sampling where the study characters are sensitive. Due to the sensitivity of characters, practitioners don’t get the actual response. Randomized response technique (RRT) models are developed to reduce the bias raised by an evasive response on the sensitive variable. The measurement error (ME) is usually always present in the surveys so we need to study the RRT models with ME. We propose an estimator to predict the population mean of a sensitive variable in the influence of ME. The properties of the proposed estimator are studied and comparisons are made with the existing estimators. At last, a simulation study is executed to illustrate the results numerically.
This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set ... more This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.
There are situations in survey sampling where the study characters are sensitive. Due to the sens... more There are situations in survey sampling where the study characters are sensitive. Due to the sensitivity of characters, practitioners don't get the actual response. Randomized response technique (RRT) models are developed to reduce the bias raised by an evasive response on the sensitive variable. The measurement error (ME) is usually always present in the surveys so we need to study the RRT models with ME. We propose an estimator to predict the population mean of a sensitive variable in the influence of ME. The properties of the proposed estimator are studied and comparisons are made with the existing estimators. At last, a simulation study is executed to illustrate the results numerically.
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