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Generalized Designing of Systematic Sampling Schemes

Thesis Info

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Author

Khan, Zaheen

Supervisor

Javid Shabbir

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/7159/1/Zaheen_Khan_Statistics_QAU_2015_ISD.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726259147

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After a detailed review of existing sampling schemes, a new class of systematic sampling design, called a Generalized Linear Systematic Sampling (GLSS) for estimation ofnite population mean is introduced. The proposed design is found to be better than Simple Random Sampling (SRS) and is the generalization of the several existing systematic sampling schemes such as Linear Systematic Sampling (LSS), Diagonal Systematic Sampling (DSS) and Generalized Diagonal Systematic Sampling (GDSS). All of these designs become special cases of the proposed design. In this design an optimum choice of sampling interval under linear trend is also be discussed. Sampath and Varalakshmi (2008) proposed an equal probability scheme called Diagonal Circular Systematic Sampling (DCSS) under the conditions stated by Sudhakar (1978). However, it is observed that DCSS does not ful ll these conditions. Therefore, a necessary and su cient condition has been suggested for DCSS after a slight modi cation in the theorem proposed by Sengupta and Chattophadyay (1987). Under this condition, one can easily decide when and where DCSS is applicable. Some de ciencies in traditional selection procedure of circular version of systematic sampling schemes are also investigated and alternative methods are proposed. Some rules of thumb for coincidence of units in the sample are also introduced. The end corrections proposed by Bellhouse and Rao (1975) and Sampath and Varalakshmi (2008) for circular systematic sampling (CSS) and DCSS respectively are also modi ed. Theoretical selection procedure has also been established for several cyclic CSS regarding the suggestion of Sudhakar (1978). Mean and variance expressions of CSS for perfect linear trend are not available in the literature. Therefore, a new approach is introduced to study the characteristic of circular version of systematic sampling. By using it, mean and variance expressions of CSS for perfect linear trend has been derived. Mean and variance of DCSS can be deduced from these expressions. Average variance expressions of corrected sample vii means for modi ed CSS and DCSS are derived under the super population model. Based on the average variances, numerical e ciency comparison of CSS and DCSS has also been carried out. In the current study a new sampling design called Modi ed Systematic Sampling (MSS) is proposed. In this design each unit has an equal probability of selection. Moreover, it works for both situations: N = nk or N 6= nk. Modi ed Systematic Sampling reduces to LSS, if N = nk and becomes CSS, if N and n are co-prime. The proposed MSS performs better than CSS in every aspect of systematic sampling, speci cally, simplicity, e ciency and even coverage of sample unit over the entire population. E ciency comparison of MSS with CSS is also carried out for natural populations. Furthermore, MSS is also studied for populations having a linear trend. Expressions for mean and variance of sample mean are obtained for the population having perfect linear trend among population values. Average variance of corrected sample mean under super population linear model and average variance of sample mean under super population auto-correlated model are also obtained. Further,numerical e ciency comparisons using these average variances are also obtained for di erent sample sizes. One of the major and long-standing problem of unbiased estimation of population variance is also discussed in the current study. In this case, the concept of multiple random start is extended from linear version (where N = nk) to the general case (where N 6= nk). As a result, a new sampling design called \Universal Systematic Sampling (USS)" is introduced. Linear systematic sampling and Simple Random Sampling (SRS) are the two extreme cases of this design. Mean and variance of mean for LSS and SRS can be extracted from the derived expressions of mean and variance of mean of USS. An explicit expressions of unbiased estimator of population variance and its variance are also derived. Finally, an e ciency comparison with SRS is also carried out for natural populations, simulated populations and population having linear trend.
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قاضی عبدالغفار مراد آبادی

قاضی عبدالغفار مراد آبادی
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Relationship Between Selected Variables of Parental Stress During Early Childhood Education

Parental stress is as experience of parents not only because of child-care, but also due to their community and environmental conditions, duties and everyday life. Research focused on investigation of stress among parents related to their children at early-childhood education and to explore the relationship between child’s behavior, parents’ expectations, family relationship, socio-economic status, social support, parental satisfaction and child’s responsibilities. All the parents of the students studying ECE at private schools in the areas of Rawalpindi constituted as the population of this research study. The target population consisted of all the parents of students from 10 randomly selected private schools of Rawalpindi. During scheduled parent-teachers meeting, the parents’ voluntary participation was demanded. Based upon their consent 145 parents of children from 10 private schools at Rawalpindi were available for the sample of study through purposive sampling. A self-developed questionnaire containing items related to seven aspects of parental stress was developed on five-point Likert scale. The data were analyzed with the help of descriptive mean, SD, and Pearson r. The current study shows that highest levels of stress among parents of these children. The economic disadvantage is also a leading cause for parental stress and minor social support tended to report extra parental stress. The results of the study highlighted the understanding of parents’ stress in ECE.

Formulation, Characterization and Pharmacokinetic Evaluation of Statistically Optimized Solid Lipid Microparticles of Cardiovascular Drugs

The use of Ivabradine (IBH) and Nebivolol (NEB) are considered as being effective and safe but their short plasma half-life and decreased bioavailability in conventional formulations demand frequent dosing which ultimately reduce patient compliance. The purpose of this research was to prepare Solid lipid microparticles (SLMs) of IBH and NEB to overcome the inadequacies associated with conventional formulation and to release drugs in a sustained fashion. Preliminary studies were performed to identify the effect of independent variables like concentration of lipid polymer like beeswax (BW), carnaubawax (CW), stearic acid (St-A), Glyceryle monostearate (GMS) and surfactant like tween 20 (T-20) and tween 80 (T-80). IBH and NEB loaded SLMs were designed in five different batches with different concentrations of a single or combination of lipid polymer by simple melt emulsification technique and solvent evaporation method. Central composite Rotatable Design (CCRD) was applied on every batch of SLMs to study the impact of three independent variables on responses like percentage yield (Y1), entrapment efficiency-EE-(Y2) and drug release (Y3) at pH 6.8 for 12hr. In every batch of SLMs, the compatibility of drugs with lipid polymer was checked by Fourier transform infrared spectroscopy (FTIR), Differential scanning calorimetry (DSC) and X-ray powder Diffractometry (XRD). SLMs were further analyzed for rheological behavior, zeta potential, size and for morphology by scanning electron microscope (SEM).The drug release data was analyzed by different kinetic models. Numerical optimization techniques were applied and an optimized formulation (OF) from every batch (total 5 optimized formulations) were further prepared and then characterized for in-vitro and in-vivo pharmacokinetic behaviour in healthy male volunteers. Before performing in-vivo drug analysis, HPLC method for the simultaneous estimation of IBH and NEB was developed and validated for linearity and range, intra- and inter-day precision, accuracy, recovery, limit of detection and limit of quantification. The experimental conditions of HPLC method were optimized by using CCRD, in which, flow rate, pH of buffer and wavelength were used as independent factors in order to optimize three dependent factors like retention time, number of theoretical plates and tailing factor of NEB and IBH. Noncompartmental model approach was used to calculate the pharmacokinetic parameters including the area under the plasma concentration–time curve from zero to infinity (AUC0-∞), Tmax, Cmax, t1/2, MRT and kel. All data was expressed as mean ± SD (standard deviation). Spherical, smooth surface SLMs having good rheological behavior were obtained. The resultant data from FTIR, DSC and XRD concluded the absence of any interaction between formulation components. Zeta-potential study confirmed better stability of optimized SLMs because of presence of negative charge on OF1 (-30mV to 52mV), OF2 (-25mV to -60mV), OF3 (-20mV-40mV), OF4 (-20mV to -40mV) and OF5 (-40 to -60). The size of SLMs ranged from ranged from 300µm to 400µm (OF1), 20µm to 120µm (OF2), 80µm to 220µm (OF3), 20µm to 100µm (OF4) and from 05µm to 20µm (OF5). The SLMs prepared from solvent evaporation technique (OF2, OF4, OF5) were found to have smaller size with smoother spherical surface as compared to SLMs (OF1) produced by simple emulsion congealing technique. The dependent variables had followed quadratic, 2F1 and linear models. The obtained outcomes of Y1, Y2 and Y3 for all of the SLMs have shown a significant dependence on formulation conditions. The Y1 and Y2 were found to be varied from 38 to 90% and 29 to 78% indicating the effect of formulation variables. The drug release Y3 was found to be 46 -88% and was significantly (p˂0.05) affected by lipid polymer concentration. The release mechanism followed the zero order and Korsmeyer-Peppas (n˃0.85) kinetic models suggesting slow erosion alongwith diffusion mechanism. A highly precise, robust, economical, specific, sensitive, less time consuming and accurate HPLC method was successfully developed and validated in mobile phase and human plasma as evident from short retention time and run time. The mobile phase consisting of mixture of acetonitrile and phosphate buffer maintained at pH of 3.5 in the volumetric ratio of 1:1 led to achievement of the best resolution. The optimized HPLC experimental conditions involve a flow rate of 1 mL/min under which, a good retention time of 3.591 minutes for NEB and 2.21 minutes for IBH was obtained. The optimized SLMs OF3 (Group C), OF4 (Group D) and OF5 (Group E) have significantly higher (P˂0.005) Cmax, Tmax, AUC0-24, MRT0-24 and t1/2 than those obtained from OF1 (Group A) and OF2 (Group B) because of use of a combination of lipid polymers. However, OF1 and OF2 were found to be better as compared to marketed brands of IBH (Group F) and NEB (Group G).The difference in Tmax, AUC0-24, MRT0-24 for OF3, OF4, OF5 was found to be statistically insignificant, however these parameters were found to be higher for OF5. The marketed brands of IBH and NEB released the drugs immediately resulting in rapid drug absorption with lower Tmax and lower AUC values. Results of the study clearly depicted the suitability of lipids as carriers for designing a controlled release SLMs which would definitely increase the clinical utility of IBH and NEB to improve the patient compliance by decreasing dosing frequency and drugs associated side effects particularly in the cases of chronic illnesses like Hypertension. The results of pharmacokinetic analysis were quite suggestive of prominent effect of SLM formulations on in-vivo behavior of drugs and they can be considered a prospective administration system for once-a-day oral administration of a medicament. Key Words: Beeswax, Carnauba wax, Central composite rotatable design (CCRD), DSC, FTIR, Glyceryle monostearate, HPLC, Ivabradine, Melt Emulsion Congealing Technique, Nebivolol, Solid Lipid Microparticles, Solvent evaporation process, Stearic acid, XRD.