In this paper we have explored a new discrete probability mass function that has been generated through compounding mechanism. This newly proposed probability mass function is essentially a mixture of Poisson and Ailamujia distribution. Furthermore the parameter estimation has also been discussed by using Maximum likelihood estimation (MLE) technique. Moreover, we have also studied some important properties of the proposed model that include factorial moments, raw moments, mean, variance, and coefficient of variation. In the end, the application and potentiality of the proposed model have been tested statistically and it has been shown that the proposed model can be employed to model a real life data set to get an adequate fit that has also corroborated through graphically.
There are diverse lifetime models available to the researchers to predict the uncertain behavior of random events but at times they fail to provide adequate fit for some complex and new data sets. New probability distributions are emerging as lifetime models to meet this ever growing demand of modeling complex real world phenomena from different sciences with better efficiency. Here, in this manuscript we shall compose Ailamujia distribution with that of power series distribution. This newly developed distribution called Ailamujia power series distribution reduces to four new special lifetime models on simple specific function parametric setting. Apart from this some important mathematical properties in the form of propositions will also be discussed. Furthermore, characterization and some statistical properties that include mgf, moments, and parameter estimation have also been discussed. Finally, the potency of newly proposed model has been analyzed statistically and graphically and it has been established from the statistical analysis that newly proposed model offers a better fit when it comes to model some lifetime data set. Mathematics Subject Classification 2000: 62EXX
Purpose: Osteoarthritis (OA) of the knee is one of the major causes of locomotive syndrome, defined as being restricted in one's ability to walk owing to a dysfunction in one or more parts of the motor organs. In the diagnosis and treatment of knee OA, information for gait of patients with knee OA is important. Although the gait of patients with knee OA can be measured using motion capture technology, the devices currently available require a huge space to monitor and scan the patient's motion, making it difficult to use in the clinical setting. The aim of this study was to establish a novel motion capture technology developed by HITACHI Ltd. to monitor the walking ability of patients with knee OA in the clinical setting. Methods: This study was approved by institutional ethical review committee in our university. Eight painful medial knee OA patients with Kellegren-Laurence (K/L) grade 4 scheduled for primary total knee arthroplasty (TKA) and was able to walk 30m were enrolled in this study (mean age 74.7 y, male/female 4/4). The eye-opened one leg stance time, time up and go (TUG) and 30m walking before TKA operation and 2 weeks after operation was measured wearing the novel devices. This device consists of linked stays and insole-type pressure sensor arrays. The stays have inertial sensors (accelerometers and gyroscopes) to measure the hip joint angles, and potentiometers to measure the knee joint angles. The pressure sensor arrays which are inserted into the shoes measure the balance (center of pressure) of the patients while they walk. These light weight (350 g including shoes) and small (3 x 5 x 2 cm) devices can measure the gait and send the results to a PC without the need for a video monitoring system. Results: We had confirmed the accuracy and safety of this device for the gait analysis. We could measure sagittal plane hip and knee joint angles, plantar partial pressure and movement of center gravity. In the operated side, double knee action that presented in the normal knee disappeared before TKA operation, but recovered 2 weeks after TKA operation. Eye-opened one leg stance time in 2 weeks after TKA operation was also improved than it before operation. However, there were TUG improvement group and non-improvement group before and after operation. The range of motion of the operated side of the hip joint and the walking stride at the time of 30m walking had both significantly improved in the TUG improvement group than in the TUG nonimprovement group (p ¼ 0.008 and 0.002, respectively). Conclusions:We demonstrated the possibility that the novel miniaturized motion capture technology could monitor the walking ability of patients with knee OA in the clinical setting. We also demonstrated in the present study that the range of motion of hip joint and the walking stride were the factors that related early postoperative walking recovery by analyzing gait analysis before and after TKA in end-stage knee OA.Purpose: At the moment animal models for osteoarthritis (OA) lack the possibility to observe the activity...
The present paper introduces an advanced five parameter lifetime model which is obtained by compounding exponentiated quasi power Lindley distribution with power series family of distributions. The EQPLPS family of distributions contains several lifetime sub-classes such as quasi power Lindley power series, power Lindley power series, quasi Lindley power series and Lindley power series. The proposed distribution exhibits decreasing, increasing and bathtub shaped hazard rate functions depending on its parameters. It is more flexible as it can generate new lifetime distributions as well as some existing distributions. Various statistical properties including closed form expressions for density function, cumulative function, limiting behaviour, moment generating function and moments of order statistics are brought forefront. The capability of the quantile measures in terms of Lambert W function is also discussed. Ultimately, the potentiality and the flexibility of the new class of distributions has been demonstrated by taking three real life data sets by comparing its sub-models.
The present paper introduces an advanced five parameter lifetime model which is obtained by compounding exponentiated quasi power Lindley distribution with power series family of distributions. The EQPLPS family of distributions contains several lifetime sub-classes such as quasi power Lindley power series, power Lindley power series, quasi Lindley power series and Lindley power series. The proposed distribution exhibits decreasing, increasing and bathtub shaped hazard rate functions depending on its parameters. It is more flexible as it can generate new lifetime distributions as well as some existing distributions. Various statistical properties including closed form expressions for density function, cumulative function, limiting behaviour, moment generating function and moments of order statistics are brought forefront. The capability of the quantile measures in terms of Lambert W function is also discussed. Ultimately, the potentiality and the flexibility of the new class of distributions has been demonstrated by taking three real life data sets by comparing its sub-models.
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