Department of Statistics
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Item 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 SanaullahIn 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 literatureItem INTERNSHIP AT AUR-LAB(Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) FAZEEL UMAR; FA20-BST-002; Dr. Mian Muhammad FarooqAUR Lab is a cooperative venture between Predominant College, as of now positioned No. 1 private for influence among private colleges in Pakistan (QS Positioning), and We-Plan, an Australian plan firm working in Pakistan. In the span of 10 months of foundation, it has accomplished the achievement of one of its startup projects being shortlisted among top two out of roughly 100+ entries from Pakistan in the Endeavor Cup Global contest. Current undertakings are managing in various business ventures, including archeological the travel industry; Metaverse; NFT Commercial center; administration and casting a ballot; Style plan; healthcare; Shrewd Agrarian; environmental the travel industry; structural plan; AR-based promoting; energy effectiveness; street wellbeing; orientation equity; also, land income. Our group of specialists incorporates specialized staff as well as business improvement staff: Dr. Muhammad Ashraf Khan; Prof. Saleem Zubair; Ms. Qurratulain Sonia Kashmiri; Mr. Muhmmad Ahmad; Mr. Jawad Ahmad; also, Mr. Javaid IqbalItem 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 MohsinProbability 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.Item INTERNSHIP ON AUR-LAB(Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) Muhammad Samran; FA20-BST-003; Dr. Muhammad Noor-ul-AminAUR-LAB is a collaboration between Superior University, which is presently ranked first in Pakistan for effect among private universities (QS Ranking), and we Plan, an Australian design business based in Pakistan. Within 10 months of its inception, one of its startup initiatives was selected as one of the top two out of about 100+ proposals from Pakistan in the Venture Cup International competition. Current projects include archaeological tourism, Metaverse, NFT Marketplace, governance and voting, fashion design, healthcare, Smart Agriculture, ecological tourism, architectural design, AR-based advertising, energy efficiency, road safety, gender equality, and land revenue. Dr. Muhammad Ashraf Khan, Prof. Saleem Zubair, Ms. Qurratulain Sonia Kashmiri, Mr. Muhmmad Ahmad, Mr. Jawad Ahmad, and Mr. Javaid Iqbal are among our technical and business development professionals.Item Development of Modified MaxAEWMA Control Chart based on Auxiliary Information(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Zainab Manzoor; SP19-RST-004; LHR TP 6536; Dr. Tajammal HussainGlobalizations and streamlined commerce have opened the entryway of worldwide open market rivalry that changed the organization of working together. Open rivalry has an extreme impact on neighborhood market makers and worldwide firms. From the earliest starting point, quality is considered as a pre-essential definitive component to choose items or administrations. Presently days, the associations put more into observing and improving the nature of the items to draw in more clients. Besides, the basic considering purchasers has changed now they request a higher caliber of items and administrations. Walter A. Shewhart (1920) presented the idea of Statistical Quality Control (SQC), which is a coordinator of the quality control field. The crucial target of SQC is to zero in on the nature of the assembling mechanism to accomplish the most noteworthy creation quality. As per Montgomery (2009) in statistical mechanism control, each made item is not the same as one and another due to normal inborn variety, however with unnoticeable variety. The vast majority of organizations are putting resources into the quality enhancements division to decrease squandered items. The decrease in changeability builds the benefit of association and fulfillment of clients by satisfying their needs. As observed from the shopper's conduct a high variety of items is unsuitable for them, consequently, the objective of associations is to create items by stable mechanism.Item Generating New Class of Distributions(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Ahtasham Gul; FA13-PSTAT-001; Muhammad Mohsin; LHR TP 7741Probability 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 highlightedItem Spatial and Temporal Analysis of Drought(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2023) Muhammad Furqan Ahmad; CIIT/FA19-BST-002/LHR; Dr. Mian Muhammad Farooq; LHR TP 9937In the recent years climate change is the hot topic of research. Climate change can have severe effect on the environment. The drought is an important factor of the climate. If a drought occur in some area it will affect the agriculture, water resources and other important factors of the country. In this study, the impact of drought in different districts of Punjab, Pakistan was studied using Standardized Precipitation Index (SPI) and Standardized Anomaly Index (SAI). The SPI is applied on the rain data and the SAI was applied on the temperature data. The data was collected from Pakistan Metrological Department. At first, we fit the data on Length Biased Exponential Distribution and then we applied Standardized Precipitation Index on the rain data received from Pakistan Meteorological Department from 1993 to 2022. We also computed SPI using 3-month, 6-month, and 12-month moving average of the original data. We conducted spatial and temporal analysis using SPI and for the visual representation we also plot maps of the past five years for better understanding of the drought. Standardized Anomaly Index (SAI) is a useful tool to measure and monitor deviations from normal conditions in terms of temperature or other relevant variables associated with drought. We used temperature to better explain the drought impact in Pakistan. After applying SAI, we find out that temperate of the data is above average which means there is drought impact in different districts of Pakistan. The results show the clear drought pattern in different districts of Pakistan. We ignore the 0 and negative values of rain data before fitting the Length Biased Exponential Distribution as it is undefined for these values and then we compute the results. The graphs show that after taking moving average the drought patterns decrease in districts and also few years does not show any drought pattern.Item EBIZ Lounge Private Limited(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Sehar Shabbir; CIIT/FA21-BST-011/LHR; Dr. Tajammul Hussain; LHR TP 9931EBIZ LOUNGE (PRIVATE) LIMITED, a well-established service company with over two decades of experience, has built a strong reputation in the industry in Pakistan by consistently delivering high-quality services to its clients. The report includes an introduction to the company, along with an overview of its organizational structure, competitive strategy, and core business operations. A brief SWOT analysis is also provided, highlighting the strengths, weaknesses, opportunities, and threats facing the organization. The final section covers the responsibilities that were assigned, the knowledge gained from the experience, and some of the challenges encountered during the internship. Through the internship at EBIZ LOUNGE (PRIVATE) LIMITED, valuable exposure to the exports industry was gained. The insights and expertise acquired throughout the experience added to the professional growth, providing the opportunity to apply the knowledge learned through education.Item A study of ordered random variables for Reflected Power Function Distribution(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Maydah Azhar; CIIT/FA20-BST-008/LHR; Dr. Riffat Jabeen; LHR TP 9953This thesis presents a comprehensive study of ordered random variables for the Reflected Power Function Distribution (RPFD). The primary focus is on the statistical properties, parameter estimation methods, and applications of the RPFD. The RPFD is a transformation of the traditional Power Function Distribution, which is frequently used to model phenomena in various fields such as hydrology, economics, and engineering. By reflecting the distribution around its midpoint, the RPFD provides a mirrored perspective that is particularly useful for scenarios where probabilities are skewed in the opposite direction. The study begins with an introduction to the Power Function Distribution and its reflection to form the RPFD. The properties of the RPFD, including its probability density function, survival function, hazard rate function, and moments, are thoroughly explored. Various parameter estimation techniques such as Maximum Likelihood Method (MLM), Modified Maximum Likelihood Method (MMLM), and percentile-based estimators are discussed in detail. Furthermore, the thesis delves into generalized order statistics (GOS) and their specific application to the RPFD. This includes the derivation of the probability density function (PDF) and joint PDF for GOS, as well as the calculation of mean, variance, and covariance for different scenarios. The literature review highlights key studies and methodologies that have contributed to the development and understanding of order statistics and RPFD. Empirical analysis using real-life data sets demonstrates the practical utility and superior performance of the RPFD compared to other models. Overall, this research contributes to the statistical theory by providing new insights and tools for the application of the RPFD in various scientific and engineering disciplines.Item Modified Radial Basis Function Network (RBFN) by Bayesian Regression for predicting Synthetic Cancer(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Fazeel Umar; CIIT/FA20-BST-002/LHR; Dr. Mian Muhammad Farooq; LHR TP 9948This thesis investigates the use of Long Short-Term Memory (LSTM) networks to predict Google’s stock prices. The study focuses on stock data from January 2012 to December 2016 for training, and January 2017 for testing. LSTM, a type of Recurrent Neural Network (RNN), is ideal for time series forecasting because it can learn long-term dependencies. To prepare the data, stock prices were normalized using Min Max Scaler, which helps improve model performance. The data was then organized into sequences of 60-time steps using a sliding window approach. The LSTM model was built with four layers, each containing 50 units, and included dropout layers to reduce overfitting. Training was conducted using the Adam optimizer and mean squared error as the loss function over 100 epochs with a batch size of 32. The results showed that the LSTMmodel effectively captured the stock price patterns, highlighting its potential for accurate financial forecasting.