Department of Statistics

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Start date: 2020Subject: search.filters.subject.Statistics

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    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.
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    INTERNSHIP AT AUR-LAB
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) FAZEEL UMAR; FA20-BST-002; Dr. Mian Muhammad Farooq
    AUR 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 Iqbal
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    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.
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    INTERNSHIP ON AUR-LAB
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) Muhammad Samran; FA20-BST-003; Dr. Muhammad Noor-ul-Amin
    AUR-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.
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    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
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    INTERNSHIP REPORT ON BAIG ELECTRICAL COMPANY (PVT.) LIMITED
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Fakhra Manzoor; CIIT/FA21-BST-009/LHR; Dr. Riffat Jabeen; LHR TP 9957
    When I was working as an intern in Baig Electrical Company (Pvt.) Ltd., I was blessed to work with an organization that was electrical based and I was able to develop on several of these skills. The type of tasks included data entry and auditing; in this way, I gained knowledge of the finance department. The management practices that were explained to me were useful in realizing that people have various responsibilities within a firm. I have appreciated various aspects of how a business runs and the many roles I can take on depending on the sector. In the course of my internment, I engaged myself with multiple exercises that were entirely a new and unique experience to me. They allowed me to participate in testing processes, which provided me with practical experience that I needed. I also came to appreciate quality assurance and got to deal with transformers and switch gears, which I found out are among the company’s biggest brands in the market. This exposure has given me this information on the competition in the electrical sector. I understood the importance of product quality and safety standards in situation to the electrical field which are the critical factor of electrical products and systems’ reliability and safety. It equipped me with technical know-how in and out, soft skills as a team player, good communicator and critical thinker.
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    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 9937
    In 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.
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    INTERNSHIP REPORT OF BUREAU OF STATISTICS, GOVERNMENT OF PUNJAB, LAHORE
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Shafaq Ikram; CIIT/FA21-BST-021/LHR; LHR TP 9933
    The Bureau of Statistics (BOS) of the Government of Punjab plays a pivotal role in the collection, processing, and dissemination of statistical data within the province. Operating under the Department of Planning and Development, BOS is responsible for ensuring that statistical activities are conducted in accordance with the standards set by the National Statistical Council. Its primary functions include the collection of provisional data in standardized formats, coordination of statistical activities both within the province and in relation to the federal statistical system, and the provision of comprehensive statistics through collaboration with various cognate institutions. Additionally, BOS is tasked with conducting new censuses and surveys to enhance the availability of reliable data. This extensive infrastructure enables BOS to effectively gather and disseminate statistical information that is crucial for informed decision-making and policy formulation. Pakistan's statistical system has its roots in a decentralized framework established at the time of independence in 1947. Initially, statistical activities were primarily viewed as a utility for administrative functions. The Central Statistical Office (CSO) was established in 1950 as an Attached Department within the Economic Affairs Division, taske
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    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.
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    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.