Department of Statistics

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Ratio & Product estimators of mean using two-phase sampling in the presence of non-response
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Irfa; FA14-MSSTAT-001; Dr. Muhammad Ismail; LHR TP 4483
Many statisticians have been worked in the field of two-phase sampling when there is a non-response in the data using a single auxiliary variable and multi-auxiliary variables for different cases which begin since Hansen and Hurwitz’s (1946) work on non response. In this study, new estimators of mean in the form of ratio and product are proposed for different cases of two-phase sampling using a single auxiliary variable for non-response. The mean square errors expressions of the proposed estimators are also derived. An empirical study is also conducted to assess the performance of the proposed estimators with existing estimators
GENERALIZED ESTIMATORS OF POPULATION MEAN IN TWO PHASE SAMPLING IN THE PRESENCE OF NON RESPONSE
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Taimoor Safdar; FA14-MSSTAT-003; Dr. Muhammad Ismail; LHR TP 4484
In the mid of 1780’s, the famous mathematician Pierre Laplace thought to approximate the total French people by using the identified number of childbirths in a specified year and the estimated ratio of the population to annual births on the basis of population sample of 700 communes. However, his projected ratio was on no occasion recycled for its inventive purpose because it became problematic to obtain an appropriate total of childbirths for the entire French people due to many reasons including the military events against France during Napoleon’s early years.
Development of Estimators for Population Mean of Sensitive Variable in Survey Sampling
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Muhammad Kamran ASLAM; SP16-RST-005; LHR TP 4833; Dr. Riffat Jabeen
In Chapter 1, introduction about Survey sampling, use of auxiliary in formation in context stratified random sampling has been deliberated. Further in Chapter 1, Different methods dealing randomized response have been deliberated by different authors but Hansen-Hurwitz sub sampling has been consider in more detail. In Chapter 2, the literature regarding the use of classical sampling de sign has been deliberated. The literature about some existing estimators for calibration estimator under stratified random sampling has been ex press. Various work of randomized response has also been specified in Chapter 2. Some well-known existing randomized response model, scrambling vari able under auxiliary and study variable, with randomized response or complete response have been reproduced in Chapter3. The major con tribution of this study starts from next Chapter. In Chapter 4, new estimators using auxiliary information have been proposed for calibration estimator in randomized response under strat ified random sampling scheme. The mean square error each estimator has been derived along. In Chapter 5 conclusion has been drawn about the generalized class of estimators proposed in this study. Finally it is shown that the propose estimator II is more efficient than proposed estimator I.
A Four-Parameter Generalized Burr Distribution and Its Applications
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Sadia Sarfraz Khan; SP17-RST-002; LHR TP 5325; Dr Muhammad Mohsin
We study a new distribution called “A Four Parameter Generalized Burr Distribution” and present a detailed account of some of its structural properties including the r-th moment, moments about mean, skewness, kurtosis, and order statistics. The parameters of the under study distribution are estimated by the maximum likelihood method. The simulation study is also carried out under for different sample sizes to test the effectiveness of this model. Finally, the performance of the model is checked by using the real data set and comparing it with other known distributions.
Development of Fuzzy X ̅-S Control Charts through incorporating Fuzziness in Conventional X ̅-S Control Charts
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Nabila Ali; SP17-RST-006; LHR TP 5324; Dr. Tajammal Hussain
The mission to progress the quality and productivity of products and services is spreading across the industry and services sectors. Statistical process control (SPC) is a methodology to monitor an ongoing process and to identify unusual patterns and to indicate the need for correction. The most common SPC tools to be used are control charts. Control charts indicate whether or not the process is stable and resulting quality improvement. Control charts help to distinguish between special and common causes of variation which may occur during manufacturing process and influence the quality of a product.
Estimation of Population Mean by Using Robust Regression
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Salah ud din Asghar; SP16-RST-003; LHR TP 5250; Dr. Muhammad Noor-ul-amin
In the linear regression problems, ordinary least square (OLS) estimates violate in the presence of outliers as according to the assumptions of the OLS model that there should not be outliers in the data. More specifically, since the classical procedures are not applicable to the case of outliers presence. So, for the purpose of estimation there is another approach which handles this situation of outliers that is robust regression. Robust regression is an important tool for investigating data that are tainted with outliers and provide efficient results. In robust regression, estimates completely reject the effect of outliers and provide good estimates of the population parameter. In this work we focus on the problem of outliers occur in the data which provides a bad estimate of the population mean. In this dissertation, redescending M-estimator and ratio estimator have been proposed to estimate finite population mean using the information from auxiliary variable. Discussions have been made about the robust estimation method based on M-estimation, outliers, ratio estimators and auxiliary variable in Chapter 1. The literature about the robust regression and ratio estimator is discussed in Chapter 2. This research work is based on the two main chapters. The 3rd and 4th Chapters are the most important chapters of the thesis. For the first strategy, in the 3rd Chapter a redescending M-estimator is proposed by reworking on the redescending M-estimator proposed by Insha-ullah et al. (2006) which assign a weight closer to zero to the extreme values and closer to one to the good observations. Most of the redescending M-estimators are solved by iteratively reweighted least square method. For the second strategy we adopt the ratio estimators proposed by Kadilar and Cingi (2004) in the 4th Chapter and replace OLS coefficient with our redescending M-estimator proposed in 3rd Chapter in these ratio estimators. In both parts numerical illustrations and simulation studies were used to analyze the results of the proposed estimators with the comparative estimators to achieve the main results of the research. The intention of this research is to analyze, introduce and improve robust estimation methodologies to solve real life problems such as outliers in data. And finally in 5th chapter conclusion is written based upon whole the results of research.
Some New Insights of Exponential Weighted Moving Average Control Chart with Fuzzy Control Lenses
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Javed; SP16-RST-001; LHR TP 5249; Dr. Tajammal Hussain
Statistical process control (SPC) is an approaching path that analyzes processes despite the fact whether they are under statistical control or out of control. So, Control charts are commonly employed for this purpose. Possibly, sample data may possess some uncertainties occurring owing to systems of measurement and conditions of the surrounding environment, for this purpose fuzzy numbers or language variables are usable to seize such form of uncertainties. Thereby, the well-known control charts, exponentially weighted moving average control chart (EWMA) to univariate data are formed up under the environment that is fuzzy one. The fuzzy EWMA control charts (FEWMA) are also usable in order to detect minute changes in the data presented by fuzzy numbers. FEWMA lessens various mistaken and unreliable decisions by catering further flexibleness upon the control limits. As far as the production process is monitored and controlled by dint of FEWMA control chart.
Estimation of Mean for a Finite Population Using Sub Sampling of Non-Responden
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Iqra Ehsan; SP16-RST-004; LHR TP 4834; Dr. Aamir Sanaullah
In Chapter 1, introduction about Survey sampling, use of auxiliary information in context of single and two-phase sampling has been deliberated. Further in Chapter 1, the problem of non-response in two has been deliberated. Different methods dealing non-response have been deliberated by different authors but Hansen-Hurwitz sub-sampling has been deliberated in more detail. In Chapter 2, the literature regarding the use of classical sampling design has been deliberated. The literature about some existing estimators for single and two-phase sampling has been deliberated. Various work of non-response has also been specified in Chapter 2. Research methodology of proposed work has been given in chapter # 3. The major contribution of this study starts from Chapter 4 & 5. In chapter 4, we proposed some estimators using single auxiliary variables when population mean of auxiliary variable is available under simple random sampling in the occurrence of non- response. Further the properties of the proposed class of estimators have been deliberated in chapter 4. Also optimum conditions for which proposed class of estimators has minimum MSE’s has been deliberated with their empirical studies. In chapter 5, we proposed some estimators using single auxiliary variable when population mean of auxiliary variable is not available in prior under simple random sampling in the occurrence of non- response. Further the properties of the proposed class of estimators have been deliberated in chapter 5. Also optimal conditions for which proposed class of estimators attain minimum MSE’s has been deliberated with their empirical studies. In Chapter 6 conclusion has been drawn about the generalized class of estimators proposed in this study. Finally it is shown that the proposed estimators are more efficient as compare to the existing estimators of literature
Generalized Ratio Type Exponential Estimators for the Population Mean Using Ranked Set Sampling
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Amjad Ali; SP16-RST-002; LHR TP 4837; Dr. Muhammad Ismail
The dominance of using ranked set sampling, for estimating the mean of a population, as compare to simple random sampling is well reputable. This technique is useful when visual ordering of a small set of size “m” can be made simply and precisely, since exact measurement of a value is most of the times very hard to obtain. In this dissertation, exponential ratio type estimators are proposed for evaluating the population mean by using ranked set sampling. We found through numerical results that the results of proposed ratio type estimators which is estimated under ranked set sampling is more reliable and competent than the simple random sampling (SRS) and some other already existed estimators under SRS are suggested by Cochran (1977), Parsad 1989, Bahl and Tuteja (1991). The comparison is also made with estimators under ranked set sampling by Samawi and Muttalak (1996), Rabail (2014) and Gajendra , Zeeshan and Carlos (2017).
Hybrid Exponentially Weighted Moving Average Control Chart Using Ranked Set Sampling
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Navara Shabbir; SP17-RST-001; LHR TP 5301; Dr. Muhammad Noor-ul-Amin
In manufacturing process, the products are subjected to variations which directly impact the quality of a product e.g. in the process of filling juice bottles, the amount of juice filled may not exactly the same. Quality control combined with statistical techniques is called statistical process control (SPC). To achieve the level of perfection in a production procedure SPC play an important role, it generally contains tools for monitoring the dissimilarities caused during a production process. SPC has a direct impact in increasing the quality of a product by reducing the amount of variation and enabling it to attain desired satisfaction level.
Estimation of Population Mean of a Sensitive Variable under Systematic Sampling
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Kamran Khan; FA16-RST-002; LHR TP 5310
In this research study, we consider the problem of mean estimation of a sensitive variable under systematic sampling. The estimator based on one auxiliary variable is proposed for the sensitive variable under systematic sampling. Further, estimators are studied in the presence of non-response. The mean square error (MSE) expressions are derived and efficiency of proposed estimator is proved by conducting simulations.
Revisiting the Process Capability Indices (PCIs) for the Uni-variate Variable Control Charts by Incorporating the Concept of Fuzziness
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Muhammad Usman Aslam; FA17-RST-001; LHR TP 5742; Dr. Tajammal Hussain
With the passage of time and global development in the industrial world, the competition for the quality improvement of the manufactured product has also increased. To achieve the quality perfection goal the best utilized technique is quality control. The technique of quality control is merged with the statistical methods to obtain a reliable source for updating and improving the product’s quality and services, it also helps to maintain the actual quality standard. This combination of quality control with the statistical methods is called Statistical Quality Control (SQC). The concept of Statistical Quality Control (SQC) was introduced in 1924 by Dr. Shewhart who is well known as the father of quality control analysis. The principle objective of SQC is to focus on the quality of any organization and to achieve the optimum quality of production as well as services by using the sufficient statistical techniques. According to (Montgomery, 2009) any products quality depends upon its fittness for use and it is judged by the appropriate quality characteristics.
Induction of Measurement Error in Acceptance Sampling Plans
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Sajid Ali Naqvi; SP17-RST-004; LHR TP 5741; Dr. Muhammad Noor-ul-Amin
Measurement error practically exists to a certain degree and part and parcel of measurement process for quantitative observations. Measurement error cause contamination and result in ineffectiveness of the scale sampling plan. In present study the effect of measurement error is investigated for EWMA based scale sampling plan using a linear covariate method when population standard deviation is known or unknown. The same effect is also examined in the presence of auxiliary information when measurement of quality characteristic is not feasible or accessible. Multiple measurements method is a remedy to minimize the effect of measurement error. The variance of measurement error component becomes zero for infinite number of multiple measurements. A reasonable and economical number of multiple measurements may restore the effectiveness and utilization of EWMA based scale sampling plans with or without auxiliary information when population standard deviation is known or unknown. Tables are provided for various values of model parameters for industrial use
Bayesian Estimation of Inverse Rayleigh Distribution using Truncated Inverted Gamma as a Prior with different Loss Functions
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Sehrish Liaquat; FA17-RST-003; LHR TP 5744; Dr. Muhammad Mohsin
We introduce the truncated prior in Bayesian analysis to refine the posterior distribution and get improved results. The parameter of Inverse Rayleigh (IR) distribution is estimated through Bayesian approach using various loss functions such as squared error loss function, entropy, general entropy, precautionary and squared log error loss function. Two types of Bayes estimators of the posterior expected risks for each loss function i.e. the truncated prior with the proper sampling distribution and the prior as a proper pdf with truncated sampling distribution are studied. In addition, the equal-tail credible intervals are constructed for all the cases. The simulation study is conducted to compare the different Bayes estimators along with the different procedures to seek the best estimators. A real life example is also presented to support the performance of the proposed technique.
Generating New Class of Distributions
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Ahtasham Gul; FA13-PSTAT-001; Muhammad Mohsin; LHR TP 7741
Probability distributions analyze the variability in real life problems systematically by providing appropriate models. These models are capable of handling the complex situations and draw useful inferences. In spite of immense work on probability distributions in literature, the development of new models and modifications of the existing models are made out continuously even today. In the similar vein, truncated distributions have their own importance in modeling the real life data in these days due to limited resources, time and expenses. Generally, the probability distributions apply to infinite domain i.e. 0 to ∞ but there have been certain situations when we need the reduced or finite domains. The infinite domain of a probability distribution is reduced to finite domain by truncation and the resulting distribution is called the truncated distribution. Truncated distributions are constantly utilized in various fields like astronomy, medicine, epidemiology, biometry, engineering, hydrology and economy. This thesis is categorized into six chapters. Chapter 1 is introductory in nature and provides genesis of the probability distributions. A brief survey of the literature on existing truncated distributions and their applications are given. In Chapter 2, a new methodology is proposed for generating a new family of truncated distributions and its general mathematical properties are derived. Some families of generalized truncated distributions for different XT distributions are tabulated. In Chapter 3, Gumbel-Truncated exponential distribution is developed by using the proposed methodology. The structural and statistical properties including moments, moment generating function, entropy, hazard function and order statistics are derived. The parameters are estimated by using maximum likelihood estimation technique. The simulation study is carried out to examine the performance of the proposed distribution. The proposed truncated model is fitted on real-life data sets to highlight its compatibility. In Chapter 4, another life time model i.e. Half logistic-Truncated exponential distribution (HL-TEXPD) is developed by using the proposed methodology and its various statistical properties have been studied. The parameters are again estimated by using maximum likelihood estimation technique. HL-TEXPD is fitted on real-life data sets to check its applicability. In Chapter5, the recurrence relations for HL-TEXPD are established for the single and product moments of order statistics for various values of scale parameter θ. These recurrence relations are used to calculate the first k moments of all order statistics in a simple xi and efficient manner and tabulate means, variances and co-variances, percentage points of the extremes and modes of all order statistics for samples of size n=1(1)10 for different values ofscale parameter. In Chapter 6, the thesis is summarized and some new directions for future research are highlighted
Some Properties, Characterization and an Application of Mittag-Leffler type Poisson distribution
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) AYESHA ISRAR; SP19-RST-006; LHR TP 6537; Dr. Muhammad Mohsin
Probability distributions analyze the complex phenomena in a comprehensive way and provide the possible solutions of the understudy problem. The characteristics of a probability distribution describe its behavior and check its compatibility for modeling the data. The present research involves an extensive study of Mittag-Leffler type Poisson (MLTP) distribution developed by Porwal and Dixit (2017). They used Mittag-Leffler function, a mathematical function/series, to develop a new probability distribution. This function has been extensively used in the fields of mathematics, engineering, medical and social sciences. Some mathematical properties of the MLTP distribution are discussed. Graphical representation of MLTP distribution is provided for different values of the parameters. The moment generating function, characteristic function and order statistic are also studied. Characterizations for the sum of the random variables are presented. The distributions of product and ratio of two MLTP random variables are derived. In addition, the estimates of unknown parameters of MLTP distribution are obtained by using the method of maximum likelihood estimation. The MLTP distribution is applied to three real life data sets from the medical field. The log-likelihood values, AIC and BIC of the present model are compared with those of some other distributions extant in the literature.
On Extended Exponential Weighted Moving Average Control Charts for Monitoring Mean of a Process
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Aqsa Hussain; SP19-RST-001; LHR TP 6535; Dr. Aamir Sanaullah
In chapter 1, the introduction about statistical process control, control charts and use of auxiliary information in control charts has been explained. Further in chapter 1, objectives of control charts also described. Objectives of the proposed study explained in chapter 1. In chapter 2, literature about some existing EWMA-type control charts has been provided. Various works of EWMA-type control charts using auxiliary information have also been specified in chapter 2. In chapter 3, an extended-EWMA control chart by Naveed et al. (2018) has been discussed. Further a EWMA control chart based on the auxiliary variable due to Abbas et al. (2014) for mean has been deliberated. In chapter 4, we are working on EEWMA control chart by using an auxiliary information for improving the efficiency of an extended-EWMA control chart due to Naveed et al. (2018), and then comparison of the proposed EEWMA with the existing EEWMA and EWMA control charts is presented. In chapter 5, we propose EEWMA sub-group mean control charts for mean with or without using auxiliary information to detect smaller shifts earlier. Comparison with the previous control charts is also done in this chapter. Finally it is shown that the proposed EEWMA control charts are more efficient as compare to the existing control charts of literature
The Impact of Socioeconomic Factors and Parental Involvement on Functional Challenges of Children
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-02-01) Muhammad Samran; CIIT/FA20-BST-003/LHR; Dr. Muhammad Noor ul Amin; LHR TP 9949
Functional difficulties that children experiencing today is including a range of cognitive and emotional,; social and behavioral problems greatly affect there academic performance as well as their ability to form appropriate relation and adjust overall. The problems regularly continue into adulthood with consequences on multiple areas of life. By the; understanding the more various factors of irresponsibility is very much important for successful joining and assistance. Having this complexity or challenge the purpose of the study was to illuminate how parental participation and socio-economic status are linked and impact childrens function. In actual it has always been common knowledge that the quality of education; opportunities for personal growth also access to resources are directly dependent on socioeconomic factors which have also remained importance in measuring childrens development. Children coming from socioeconomically disadvantaged backgrounds will face more difficulties in achieving academic success and integration into the social sphere than their peers originating from families with better socioeconomic status. Similarly, parents’ involvement plays a vital role in the nourishment of children. This dimension is in line with notions of both parental support, supervision and active engagement, as they each relate to a childs educational-e x tracurricular life. Nearly all studies reveal that increased parental involvement has been linked to more favorable academic performance, better-developed socioemotional skillsets and greater general health in children. “But the critical fact we discovered was that there is a complex interplay between socioeconomic status (SES) and parental involvement. Both factors could play a role in the appearance and severity of functional problems driven by children. So, for example, parents who come from a low SES backgrounds may have less resources and time to invest in their child’s education and well-being and even make things worse in the case of functional difficulties. The underlying biological, psychological, and social mechanisms by which SES and parental involvement moderate associations with children’s functional ability are not well understood. Therefore, the present study seeks to fill this gap in literature answering whether and how SES and parental involvement interact with each other for affecting children’s functional difficulties. “Our analysis of this linkage intends to present a comprehensive understanding of the complex dynamics between children’s functional limitations, parental involvement, and socioeconomic status”.
Generalized Transmuted Exponential Distribution
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) BILAL MAJEED; CIIT/FA19-BST-008/LHR; Mr. Salman Abbas; LHR TP 9942
In this study, we use the Transmuted Family of distributions to develop a novel generalized exponential model. Transmuted Exponential distribution is the name of the suggested distribution. For the proposed distribution, moments, generating functions, reliability functions, among other mathematical aspects, are explored. The maximum likelihood approach is considered to estimate the distribution parameters. The use of the under study distribution in real-world scenarios is then explained. The proposed family can be used for the generalization of the classical models.
Development Of Calibration Log Estimator to Estimate Population Mean Using Randomized Response Technique
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) Rehmina; CIIT/FA19-BST-011/LHR; Dr. Riffat Jabeen; LHR TP 9944
Calibration method is a useful method in daily life meanwhile it allows us to gather a single sample without repeating the process. In the presence of sensitive information, we calculate the variation of population with the help of calibration method. We proposed calibration log ratio estimator by using the method of (Jabeen, et al. 2022) in the presence of sensitive data.