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Asian Journal of Probability and Statistics
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This is an Open Access Journal

Open Access journal
ISSN (Online) 2582-0230
Published by SCIENCEDOMAIN international

[66 journals]

On Propositions Pertaining to the Riemann Hypothesis III
- Authors: Pathikrit Basu
  Pages: 1 - 8
  Abstract: In this paper, we consider further propositions concerning the range of possible distributions over the unit circle, for the Riemann zeta function as in prior research. We also derive some new upper bounds on the sum of norms for the tail sequence corresponding to the Riemann zeta function. We discuss some hypotheses, conditional on which, properties of concentrated distributions may be obtained. Specific sub-classes are shown of distributions that occur infinitely often along the imaginary axis.
  PubDate: 2024-07-17
  DOI: 10.9734/ajpas/2024/v26i8634
  Issue No: Vol. 26, No. 8 (2024)
Efficiency of Modified Exponential Dual to Ratio-Product-Cum Type
Estimator under Stratified Sampling Using Two Auxiliary Variables
- Authors: Haruna Suleiman, Jibrin Abdullahi Yafu, Audu Ahmed
  Pages: 9 - 27
  Abstract: Separate and Combined dual to ratio-product-cum estimators of the population mean under stratified random sampling scheme are suggested using the ideas and the analogy of (Walsh [1], Reddy [2], Tripathi [3]) and adopted strategy initiated by (Koyuncu and Kadilar [4], Singh et al., [5], Yasmeen et al., [6], Rather and Kadilar [7]) as well as the two auxiliaries variable. Asymptotic properties of proposed estimators such as BIASs, MSEs and MMSEs up to first order of approximation by Tailor series approach were deduced and reported. Performance is evaluated and examined with others related estimators considered using empirical study utilized two natural populations and simulated data sets. The statistical package R plus is used for computations. However, Results eventually indicated the superiority of proposed estimators over existing traditional estimators mentioned in studied.
  PubDate: 2024-07-19
  DOI: 10.9734/ajpas/2024/v26i8635
  Issue No: Vol. 26, No. 8 (2024)
Three-Parameters Gumbel Distribution: Properties and Application
- Authors: Otieno Kevin Okumu, Omondi Joseph Ouno, Anthony Nyutu Karanjah, Samuel Nganga Muthiga
  Pages: 28 - 57
  Abstract: In this research, we introduced a new three-parameter Gumbel distribution by adding a parameter to the traditional Gumbel distribution using the Marshall-Olkin method. This new distribution enhances exibility and provides more ecient estimators for various data types, including normal, skewed, andextreme data. We derived the probability density function, cumulative distribution function, and other statistical properties of the new distribution. The parameters are estimated using the Maximum Likelihood Estimation (MLE) method, and thoroughly investigated the properties of the estimators, focusing on their asymptotic bias, consistency, and mean square error (MSE). Through simulation studies and real data applications, we demonstrate the superiority of the new distribution over existing models, evidenced by smaller Akaike Information Criterion (AIC) values and more efficient parameter estimates. We recommend the new distribution for future analyses, particularly for large sample sizes, and suggest further research to refine the location parameter for improved efficiency.
  PubDate: 2024-07-20
  DOI: 10.9734/ajpas/2024/v26i8636
  Issue No: Vol. 26, No. 8 (2024)
Continuous Erlang Mixtures and their Relation to Exponential Mixtures and
Poisson Mixtures
- Authors: Beatrice M. Gathongo
  Pages: 58 - 70
  Abstract: This study provides a novel method for obtaining Erlang mixtures from a mixed Poisson process. The study solved the basic differential equations of the Poisson process to obtain the Poisson distribution. The waiting time distribution in a Poisson process is illustrated as an Erlang distribution. The study also presented the Erlang mixture as the first passage time distribution in the mixed Poisson process, which was expressed using both the direct method and the method of moments. Moreover, these two ways of inferring a mathematical identity have been equated. The exponential mixture and Poisson mixture are explained as special cases of the Erlang mixture. A practical example is given, using type II gamma distribution mixtures. Properties of the mixtures, such as raw moments and probability generating function, are analyzed.
  PubDate: 2024-07-20
  DOI: 10.9734/ajpas/2024/v26i8637
  Issue No: Vol. 26, No. 8 (2024)
Monthly Rainfall Forecasting Using High Order Singh’s Fuzzy Time Series
Based on Interval Ratio Methods: Case Study Semarang City, Indonesia
- Authors: Erikha Feriyanto, Farikhin, Nikken Prima Puspita
  Pages: 71 - 88
  Abstract: Aims: Sample: To determine the effectiveness of the proposed forecasting method, namely Singh's fuzzy time series based on high order (third order) interval ratios. And find out the forecasting results in January 2022. Study Design: Modification of Singh's fuzzy time series based on interval ratios. Place and Duration of Study: Sample: monthly rainfall data for Semarang City from January 2017 to December 2021. Methodology: The method proposed by the researcher is the Singh fuzzy time series forecasting method based on high order (third order) interval ratios. This research method uses a combination of Chen and Singh's fuzzy time series. Applying Chen's fuzzy time series in the section determining the universe of discourse () to fuzzification which includes determining the universe of discourse, determining interval partitions, forming Fuzzy Logical Relationships and Fuzzy Logical Relationship Groups. Then apply Singh's fuzzy time series to the forecasting part. Finally, calculate the Average Forecasting Error Rate (AFER) to test forecasting performance. In the forecasting part, it is obtained through a heuristic approach by building high order forecasting rules to obtain better results and have an effect on very small AFER values. In the step of determining the interval partition, this research uses the interval ratio method which aims to reflect variations in historical data. Conclusion: Based on the calculation of the AFER value, the AFER for third order is 0.2422%. It can be said that Singh's fuzzy time series forecasting method based on high order (third order) interval ratios on monthly rainfall data for Semarang City from January 2017 to December 2021 is very good. And the rainfall forecast for January 2022 is 196.80 mm3 or into the category of very heavy rain.
  PubDate: 2024-07-23
  DOI: 10.9734/ajpas/2024/v26i8638
  Issue No: Vol. 26, No. 8 (2024)
Discrete Erlang Mixed Distributions and their Properties
- Authors: Beatrice M. Gathongo
  Pages: 89 - 106
  Abstract: The proposed research is on discrete Erlang mixtures. Properties of the mixed distributions analyzed include raw and central moments, which have been derived in terms of moments of the mixing distributions. Cumulants obtained from the cumulant generating functions were also used in deriving the moments. The posterior distribution and posterior moments are also among properties presented. Bayesian, moments and maximum likelihood methods have been applied in parameter estimation. Additionally, the mixture distributions have been fitted to two data sets to test their goodness of fit. Some methods and special functions used in the study are the exponential series, logarithmic series, geometric series, modified Bessel function of the first kind, and the Touchard polynomials. The discrete mixing distributions used are the geometric, Poisson and logarithmic.
  PubDate: 2024-07-29
  DOI: 10.9734/ajpas/2024/v26i8639
  Issue No: Vol. 26, No. 8 (2024)

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