A Generalized $$\alpha$$-Laplace Lévy Process

S. Satheesh

Asian Journal of Probability and Statistics, Page 13-20
DOI: 10.9734/ajpas/2022/v19i330469

Random time changed Lévy Processes are getting increased attention of late as they can account for a variety of features in data. In this article we discuss $$\alpha$$-Laplace Lévy Process and a generalization of it. Both are random time changed $$\alpha$$-stable Lévy Processes. We obtained a characterization of $$\alpha$$-Laplace Lévy Process and discuss the first passage time distribution of a generalized $$\alpha$$-Laplace Lévy Process. Interestingly, this first passage time follows a discrete distribution.

The Risk Model with a Constant Dividend Barrier Affected by a Threshold Value

Qiao Li

Asian Journal of Probability and Statistics, Page 28-41
DOI: 10.9734/ajpas/2022/v19i330471

This paper considers a new risk model with a constant dividend barrier, which the claim amount affected by a threshold value. The hypothesis of the model is presented and the integro-differential equation for the Gerber-Shiu penalty function is given. Then the linear solution of the Gerber-Shiu discounted penalty function is figured out. The paper also derives the integro-differential equation and the linear solution of the expected discounted dividend payments. An example is given too.

Slope Rotatable Central Composite Designs of Second Type

B. Venkata Ravikumar, B. Re. Victorbabu

Asian Journal of Probability and Statistics, Page 1-12
DOI: 10.9734/ajpas/2022/v19i330468

Central composite design (CCD) is the most commonly used fractional factorial design used in the response surface model. Kim [1] proposed second order rotatable designs (SORD) of second type using CCD, in which the positions of axial points are indicated by two numbers$$\left(a_{1}, a_{2}\right)$$. Kim and$$K_{0}$$ [2] introduced second order slope rotatable designs (SOSRD) of second type using CCD, in which the positions of axial points are indicated by two numbers $$\left(a_{1}, a_{2}\right)$$. In this paper, second order slope rotatable central composite designs of second type with$$2 \leq n_{3} \leq 4$$ (where $$n_{\text {s }}$$ denotes the number of replications of axial points) are suggested for $$2 \leq \mathrm{v} \leq 17$$ (v-stands for number of factors). It is observe that the value of level $$\mathrm{a}_{2}$$ (taking $$\mathrm{a}_{1}=1$$ ) for the axial points in CCD required for slope rotatability for second type is appreciably larger than the value required for SORD of second type using CCD. And also noted that if we replicate axial points $$\left(n_{9}\right)$$in SOSRD of second type using $$\mathrm{CCD}$$ then the value of $$\mathrm{a}_{2}$$ (taking $$\mathrm{a}_{1}=1$$ ) is approximately nearer to$$\mathrm{SORD}$$ value $$\mathrm{a}_{2}$$ of second type using CCD.

Circular Pattern of Temperature Changes and Its Effect on Workers’ Attitude (A Case Study of the Federal Polytechnic Offa)

Udokang, Anietie Edem

Asian Journal of Probability and Statistics, Page 21-27
DOI: 10.9734/ajpas/2022/v19i330470

This study is to determine the effect of temperature on workplace attitude, which led to the investigation of a circular pattern of temperature changes. The idea of time series data being presented in circular form since time itself rotates around the circle of a clock was the moving force in studying the pattern and behaviour of air temperature to identify peak periods. The data on air temperature (0C) in Offa was collected monthly from 2016 to 2020 from a reliable online source tcktcktck.org which tally with an available short period of temperature recorded by the Metrological Garden of Science Laboratory Department, The Federal Polytechnic Offa. While the data on workers’ attitudes was from a questionnaire with an 8.5 reliability index. The study adopted a descriptive approach in the first instance, where responses from the questionnaire were in tabular form and the monthly means temperature in a circular plot before the application of cosinor regression to the original monthly temperature data for further examinations. The result of the circular plot indicated seasonality in the data because the monthly mean temperature differs, making the plot not perfectly circular. The presence of seasonality noticed in the cosinor plot was confirmed in the cosinor regression analysis as being significant at a 5% level of significance. The temperature amplitude from 2016 to 2020 had its peaks in February when 50.9% to 56% of workers are likely to experience fatigue (exhausted). The analysis for 2016 indicates temperature amplitude in Offa at 2.30C which peaks in early February. While in 2020, the temperature amplitude of 3.80C peaks at the beginning of February. The increase between 2016 and 2020 is due to climate change. The government and other stakeholders should provide facilities to reduce workers’ fatigue and do more about climate change.

Applications in Some Area-Biased Distribution

Nuri Celik

Asian Journal of Probability and Statistics, Page 42-50
DOI: 10.9734/ajpas/2022/v19i330472

The preference of the proper distribution for modelling data is often a substantial concern to researchers and practitioners. For this reason, new statistical distributions or the generalizations of well-known distributions have been proposed for exible modeling. Weighted distributions are one of the generalization methods for these distributions. In this article, area biased beta, Rayleigh and log-normal distributions are introduced. Some main statistical properties, like probability density functions, cumulative distribution functions, moments and the estimation of the parameters of these distributions are obtained. Real data examples are used for illustration of these distributions.