Department of 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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    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.
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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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    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
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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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    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.
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    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
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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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    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.