Department of Statistics

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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.
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 9953
This 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.
An extended Marshall-Olkin simulated Pareto-exponential distribution: development, properties and application
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Fazia Shahid; FA19-RST-002; Dr. Muhammad Mohsin; LHR TP 7204
Marshal-Olkin simulated Pareto-exponential distribution (MOSPED) is a new distribution developed from simulated Pareto-Exponential distribution (SPED) by using Marshal-Olkin technique. SPED is a special distribution which emerges out as a marginal distribution of Bivariate Affine-Linear Exponential (BALE) distribution by Mohsin et al. (2014) without adopting any procedure. Some mathematical properties of the proposed distribution including moments, mean variance, incomplete moments are discussed along with its characterization. The reliability analysis of MOSPED comprising survival function, hazard function, reversed hazard function along with different types of entropies such as Renyi entropy, β-entropy and γ-entropy are presented. We also develop and discuss the distributions of series as well as parallel systems for the proposed distribution to observe the performance of each component in the product. Moreover, we estimate the unknown parameters of our model, parallel system and series system by using the method of maximum likelihood estimation for each distribution. A simulation study is performed to observe the stability and consistency of the model parameters. The application of the MOSPED is presented by using three real life data sets and its comparison with some baseline distributions is given on the basis of log-likelihood, AIC and BIC.
ANALYSIS OF RISK FACTORS CAUSING OBESITY IN YOUTH
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) Muhammad Noman Sabir; CIIT/FA19-BST-013/LHR; Nasir Inayat; LHR TP 9947
This cross-sectional study examined the problem of overweight and obesity among students at COMSATS University, Lahore Campus. A random sample of 120 youths was surveyed using a well-constructed questionnaire to identify significant risk factors associated with weight issues. The students' BMI was used to assess their weight status. Cross-tabulation and multiple linear regressions were performed to analyze the data. The results showed that waist circumference, birth weight, meals during TV viewing, time spent on sedentary activities, celebration with food, parents' BMI, and breakfast skipping were positively linked to obesity. Conversely, vegetable consumption, fruit consumption, and feeling sluggish due to overweight were negatively associated with obesity. These findings emphasize the importance of addressing multiple factors in tackling overweight and obesity among youth. Implementing interventions targeting these risk factors could lead to effective prevention and management of weight problems.
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.
BUREAU OF STATISTICS, PUNJAB
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) FIZA SALEEM; CIIT/FA21-BST-010/LHR; LHR TP 9931
The Bureau of Statistics, Punjab, operates as the principal agency for statistical data management within the province. Functioning under the Planning and Development Department, BOS Punjab is tasked with the comprehensive collection, processing, and dissemination of statistical information. This data is disseminated through periodic publications and digital platforms, ensuring accessibility and transparency. BOS Punjab’s mandate, as defined by the National Statistical Council, encompasses the collection of provincial-level data, coordination, and support of statistical activities across Punjab, and liaison with the Federal Statistical system. The organization is also responsible for preparing and diffusing provincial indicators by collecting data from various institutional sources and conducting new censuses and surveys. The Bureau’s Head Office is situated in Lahore, supported by a network of 9 divisional and 7 district field offices across the province, ensuring extensive reach and data coverage.
Calibration estimators for estimating population mean using different distance measures
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2025-04-01) Muhammad Bilal; CIIT/FA20-BST-007/LHR; N/A; LHR TP 9952
Abstract: In order to increase the accuracy of population parameter estimations based on auxiliary data, calibration is frequently utilized. To estimate the population variance, we suggested three estimators: a calibration variance estimator, a calibration exponential ratio estimator, and a calibration coefficient estimator. The suggested assessment was contrasted with those of Bhal and Tuteja (1991), Koyuncu and Kahilar (2012), and Isaki (1981). Compared to current estimators, the calibration variance estimators that are proposed perform better.
Classification of heart disease using MLP with SeLU activation function and Binary Cross Entropy as Loss function
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Nouman Ali; CIIT/FA20-BST-009/LHR; Dr. Mian Muhammad Farooq; LHR TP 9954
Multilayer perceptron are the basic components of deep learning and neural net- work characterized by their architecture of feedforwading consisting of fully con- nected neurons with the non linear activation functions.This thesis provides a comprehensive overview of MLPs,by giving detailed about their structure and com- ponents,including the input layer,hidden layers, and output layer. This explains the role of weights and bias neurons in the process of learning and adjustment of the complex pattern in data. Different activation functions which are Sigmoid, ReLU, tanh, were used, illustrating their important in non-linearity and using the model to find its relationship.The training of MLPs by using the back propagation method is thoroughly studied. This includes the forward pass,where the input data is stored and processed though the network,and the backward pass, where gradients of loss function are calculated to update the network parameters. The importance of the loss estimation and parameter updates are used in minimiz- ing the error and improving the model’s performance.Additionally, we will discuss about the important steps in data preparation, which involves the handling missing values,feature scaling, and ensuring the proper data formatting. The importance of splitting the data into training and testing is highlighted, Technique for preventing the over fitting, such as regularization,dropout, and early stopping. The guidelines for using the MLP is provided, starting with the simple one and then increasing the complexity based on different tasks.This thesis focuses on the usage of exper- imentation with various architecture,hyper parameters and optimizing the model to get the optimal results. Different techniques used for monitoring the training and the adjustment of hyper parameters are discussed, along with the methods to calculate the model accuracy and loss checking and test datasets.This thesis aims to adopt practitioners with the understanding of tools to develop robust and efficiency of model on different applications such as image recognition,NLP, and speech recognition. By following the detailed guidelines and using the best tech- niques in data preparation, training and evaluation can increase the performance of model.
Construction of Calibration Log Ratio Estimator to Estimate Population Variance
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) Khafiza Afzal; CIIT/FA19-BST-003/LHR; Dr. Riffat Jabeen; LHR TP 9938
Calibration is frequently used to improve the population parameter estimation’s accuracy using auxiliary data. In our study, we have introduced the calibration and the calibration log variance estimator for estimating the population variance. The study proposes the calibration variance log estimators using chi square distance measure and different calibration constraints respectively. Our findings indicate that the suggested calibration variance estimator performed better than the existing estimator.
Control Charts for new Reflected Pareto Distribution
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Huma Khalid; FA19-RST-007; Dr. Riffat Jabeen; LHR TP 7203
Pareto distribution has vast application in different fields of medical and engineering sciences. In this thesis, we have proposed a new Reflected Pareto Distribution (RPD) using Cohen (1973) to reflect the parameter of distribution. We derive different mathematical properties such as mean, variance, rth moment. Reliability measures are also discussed including Survival Function, Hazard function and reversed hazard function. The method of Maximum Likelihood Estimator and Modified maximum likelihood estimator is used to estimate the model parameters. We used three different data sets to show the performance of Reflected Pareto distribution over already existing probability distributions. We also construct the control charts to monitor the shape parameter for reliability processes using Shewhart control chart and Exponentially weighted moving averages control chart. We compare the performance of maximum likelihood estimator and modified maximum likelihood estimator for the shape parameter of Reflected Pareto distribution.
CRESCENT BAHUMAN LIMITED
(Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) Maydah Azhar; FA20-BST-008; Dr. Riffat Jabeen
Bahaman Limited. The purpose of this report is to demonstrate the practical application of my academic knowledge and skills in a real-world business setting. With more than 60 years of experience in industries as diverse as textiles, sugar, banking, insurance, food, agriculture and steel, Crescent Group has built a solid reputation in Pakistan's business community. Crescent Bahaman was initially formed as a joint venture between Crescent Group and Greenwood Mills. It has been wholly owned by the Crescent Group since 2001. In FY21, the Pakistan's commodities expanded by 14% insufferable from a low-base impact, coming about because of the pandemic prompted lockdown in 2020. By and large, the figures of commodities stay inside the scope of USD 22-25b, which is in accordance with the pattern of past ten years. The portion of materials in complete products has generally been 54-59%; coming in at 57% during FY21. The low-base impact was articulated in material area also, with the post-lockdown increase of around 13% in the products. Pakistan's material commodities have CAGR of 4.4% during long term period from FY19 to FY21. Inside the materials, high worth added fragment held the most extreme offer, which has been moving vertically or most recent three years, expanding from 73.9% in FY19 to 80.7% in FY21. Knitwear, readymade pieces of clothing, and bed wear comprise the significant part of this portion.
Data-Driven Sample Size Adaptation in EWMA Control Chart for Improved Monitoring
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Gulmakai; CIIT/FA23-RST-002/LHR; Dr. Muhammad Noor-ul-Amin; LHR TP 9873
Statistical Process Control (SPC) serves as a fundamental methodology for monitoring and maintaining stability in manufacturing processes. In this study, an Adaptive Sample Size-based Exponentially Weighted Moving Average (ASEWMA) control chart is proposed to enhance the detection of process shifts by dynamically adjusting the sample size in response to observed process behavior. The adaptability of the sample size enables the control chart to respond more efficiently to both small and moderate shifts while conserving computational and sampling resources when the process is stable. Further, the proposed control chart is evaluated in the presence of measurement error. The performance of the ASEWMA control chart is rigorously evaluated through extensive Monte Carlo simulations. Key performance indicators such as the Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) are employed to assess its effectiveness in various shift scenarios. Comparative analyses demonstrate that the ASEWMA chart consistently outperforms traditional control charts, including the Fixed Sample Size EWMA (FEWMA) and Variable Sample Size EWMA (VEWMA), particularly in detecting small shifts in the process mean. The findings of this research highlight the ASEWMA chart’s potential to provide a practical and efficient tool for quality monitoring in industrial settings. By achieving a desirable balance between sensitivity to shifts and computational efficiency, the proposed method facilitates the timely detection of process changes while maintaining robustness under in-control conditions
Determinants of Child Mortality in Punjab, Pakistan
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) Kashaf Zahra; CIIT/FA20-BST-006/LHR; Dr. Muhammad Noor-ul-Amin; LHR TP 9951
This research project examines the key determinants of child mortality in Punjab, Pakistan, focusing on factors such as birth order, mother’s age at birth, birth interval, premature birth, and multiple births. These findings indicate that firstborn and higher-order children exhibit higher mortality rates, which are attributed to inexperienced parenting in the case of firstborns and the dispersion of resources among siblings for higher-order children. The study showed that children born to mothers aged between 20-34 years had the highest survival rates than children born to mothers who are teenagers or mothers above 34 years. This means that the families mothers give birth within the age interval 20-34 are more likely to have low mortality rates hence the need to encourage family planning. It was also observed that both premature and multiple births are associated with high mortality rates hence there is a need to enhance quality perinatal and neonatal services. It is recommended that the Ministry of Health focuses on streamlined health policies, enhanced awareness of parents, and improved supply of resources to decrease infant mortality and promote general child health in the area. Integrated approaches, awareness campaigns, and the improvement of education and health care as well as the establishment of favorable policies are indispensable to tackle the multifaceted problem of child mortality.
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.
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.
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.
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 Hussain
Globalizations 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.
Drought Analysis using Transmuted Weibull Distribution
(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) Ali Hassan; CIIT/FA19-BST-005/LHR; Dr. Mian Muhammad Farooq; LHR TP 9940
The study aims to predict the drought analysis using monthly rainfall and temperature data. Over the past years drought is becoming important factor that is affected by climate changes in Pakistan. In this study we analyze the impact of drought in Punjab Districts. For this purpose, firstly data collected by Pakistan Metrological Department of Punjab Districts for the years 1993 to 2022 and then further competitive strategy analysis that fits our analysis or predictions are sought and critically reviewed. Then the chosen parts from strategy analysis are applied for the graphical presentation. Firstly, Applying Standardized Precipitation Index based on precipitation data by fitting transmuted Weibull distribution from the year 1993 to 2022 of each District (Bahawalnagar, Bahawalpur, Jehlum, Jhang, Lahore, Sialkot, Sargodha, Faisalabad, and Multan) to get know about classification of drought against each observed precipitation values and understand the impact of precipitation on drought. Transmuted Weibull Distribution is fitted on precipitation data to normalize it as SPI is calculated after fitting distribution on it. Further to identify trends of drought SPI calculated at different time scales by moving average of Three months, six months, and Twelve months to find SPI values and then these values are classified according to their drought conditions as moderate, severe, extreme near to normal, slightly wet, and extreme wet. Secondly applying Standardized Anomaly Index is another index that is widely used for drought analysis based on temperature data. SAI is calculated against each District (Bahawalnagar, Bahawalpur, Jehlum, Jhang, Lahore, Sialkot, Sargodha, Faisalabad, and Multan) from 1993 to 2023. By SAI values we can analyze the impact of temperature on drought. SAI values are shown in graphical form below in Chapter Results, that shows the trend and the SAI values against each year of a particular District.
EBiz Lounge (Private) Limited
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Ansa Bibi; CIIT/FA21-BST-008/LHR; Dr. Tajammul Hussain; LHR TP 9929
This internship report reflects the expert encounters and bits of knowledge acquired at EBiz Lounge Private Limited. As a Statistics student at COMSATS University, Islamabad, Lahore campus this internship offered an important chance to apply hypothetical information in a certifiable setting. The active openness in the online business, especially through association with the eBay stage, extended the comprehension of computerized commercial centers and upgraded specialized and scientific skills. The essential goal of the internship was to obtain useful involvement in overseeing item postings on eBay, advancing search engine optimization(SEO) techniques, and adding to deal development. Errands included item posting improvement, leading statistical surveying, and breaking down deals execution. Every obligation added to the proficient turn of events and gave further experiences in e-commerce dynamics. Challenges, such as adapting to changing algorithms and managing multiple priorities, offered meaningful learning opportunities. This report sums up the encounters, information acquired, and skills created during the internship. It involves the tasks which are completed in the internship, challenges I faced, and the possible solutions to get successful outcomes. Ideally, this report will act as a helpful asset for understudies and experts looking to comprehend the powerful web-based business scene and the worth of viable involvement in cultivating proficient development.
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 9931
EBIZ 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.