CAUCHY: Jurnal Matematika Murni dan Aplikasi
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Articles
438 Documents
<![CDATA[Comparing Several Missing Data Estimation Methods in Linear Regression;Real Data Example and A Simulation Study ]]>
<![CDATA[Fitrianto, Anwar]]>;
<![CDATA[Jia, Jap Ee]]>;
<![CDATA[Susetyo, Budi]]>;
<![CDATA[Rahman, La Ode Abdul]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.20548
<![CDATA[Analysis on incomplete could lead to biased estimation when using standard statistical procedure since it ignores the missing observations. The disadvantage of ignoring missing data is that the researcher might not have enough data to conduct an analysis. The main objective of the study is to compare the performance between listwise deletion (LD), mean substitution (MS) and multiple imputation (MI) method in estimating parameters. The performance will be measured through bias, standard error and 95% confidence interval of interested estimates for handling missing data with 10% missing observations. A complete empirical data set was used and assumed as population data. Ten percent of total observations in the population ere set as missing arbitrarily by generating random numbers from a uniform distribution, . Then, bias of parameter estimates and confidence interval of parameter estimates are calculated to compare the three methods. A Monte Carlo simulation was carried out to know the properties of missing data and investigated using simulated random numbers. Simulation of 1000 sampled data with 20, 50, and 100 observations and each sample is set to have 10% missing observations. Standard statistical analyses are run for each missing data and get the average of parameter estimates to calculate the bias and standard error of parameter estimates for every missing data method. The analysis was conducted by using SAS version 9.2. It was found that the MI method provided the smallest bias and standard error of parameter estimates and a narrower confidence interval compared to the LD and MS methods Meanwhile, the LD method gives a smaller bias of parameter estimates and standard error for small sample size of missing data. And, MS method is strongly recommended not to use for handling missing data because it will result in large bias and standard error of parameter estimates.]]>
<![CDATA[Mathematical Models of Human Papillomavirus Transmission with Vaccination ]]>
<![CDATA[Lobo, Maria]]>;
<![CDATA[Machado, Maria]]>;
<![CDATA[Asa, Waltrudis Adelia]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v9i1.25922
<![CDATA[The human papillomavirus (HPV) is one of the viruses that can cause cervical cancer. However, vaccination can prevent such a virus. The spread of the virus in cervical cancer can be modelled in the SI model, however, such a model has not produced accurate results. The development and extension of the model into S1S2IRC, with S1 denoting the population aged 0–10 years and S2 representing the population over 10 years, which is susceptible to HPV infection. The results produce disease-free and endemic equilibrium points. The analysis of the equilibrium points yields that the disease-free equilibrium point will be asymptotically stable for R0 1 and R0 1 for the endemic equilibrium point. The results indicate that the higher the probability of humans being prone to the HPV virus, the greater the chance of these individuals being infected by the virus. Therefore, vaccination is required to protect against the virus infection. ]]>
<![CDATA[Spatial Analysis of Dengue Disease in Jakarta Province ]]>
<![CDATA[Sobari, Muhamad]]>;
<![CDATA[Jaya, I Gede Nyoman Mindra]]>;
<![CDATA[Ruchjana, Budi Nurani]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17423
<![CDATA[Dengue disease is a virus-borne illness spread by the bite of the female Aedes aegypti mosquito. Jakarta Province has a vulnerability to dengue disease due to high population density and percentage of urban slum households. This study applied a spatial autoregressive (SAR) model to identify the risk factors that affect the number of dengue disease cases in Jakarta Province. The spatial dependency was accounted for using the queen contiguity spatial weight matrix. The number of flood-prone points, the number of slum neighborhood associations, the population density, the number of hospitals and the number of public health centers per 1,000 population and spatial lag significantly impact the number of dengue disease cases in Jakarta Province. When dengue disease cases increase in one sub-district, the number of dengue disease cases in the sub-districts around it will increase as well because of the positive and significant spatial lag coefficient. Based on the direct impact, each addition of one percent of flood-prone points in one sub-district will increase the number of dengue disease cases in that sub-district by 3.86 cases]]>
<![CDATA[Simulation Study for Parametric EWMA and NPWEWPA-SR Control Charts Against Non-Normality Assumptions ]]>
<![CDATA[Fitrianto, Anwar]]>;
<![CDATA[Choon, Lai Ming]]>;
<![CDATA[Wan Muhamad, Wan Zuki Azman]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v8i2.23315
<![CDATA[Common control chart types such as EWMA require assumptions to have valid information. The study compares IC robustness and OOC performance for parametric EWMA and NPEWMA-SR control charts in violation of symmetrical assumption. The Monte Carlo simulation study held scale parameters with various shape parameters in Weibull distribution. First finding in this paper was both parametric EWMA and NPEWMA-SR control charts were not suitable for the application in asymmetrical distribution due to weak IC robustness and frequent false alarm will be occurred. Although EWMA-X ̅ The control chart showed a most stable OOC performance; the weak IC robustness made the control chart unacceptable. Whereas, NPEWMA-SR control chart lost the ability in small shift detection when symmetrical assumption violated. Moreover, two different weightage of current sample for both parametric EWMA and NPEWMA-SR control charts were also investigated. The results showed that weightage of current sample for both parametric EWMA and NPEWMA-SR control charts did not affect the ARL value trend in different skewness of Weibull distribution.]]>
<![CDATA[Mathematical Model of Iteroparous and Semelparous Species Interaction ]]>
<![CDATA[Hasibuan, Arjun]]>;
<![CDATA[Supriatna, Asep Kuswandi]]>;
<![CDATA[Carnia, Ema]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.16447
<![CDATA[A species can be categorized based on its reproductive strategy, including semelparous and iteroparous. Semelparous species is a species that reproduces only once in its lifetime shortly before dying, while iteroparous species is a species that reproduces in its lifetime more than once. In this paper, we examine multispecies growth dynamics involving both species categories focusing on one semelparous species and one iteroparous species influenced by density-dependent also harvesting in which there are two age classes each. We divided the study into two models comprising competitive and non-competitive models of both species. Competition in both species can consist of competition within the same species (intraspecific competition) and competition between different species (interspecific competition). Our results show that the level of competition both intraspecific and interspecific affects the co-existence equilibrium point and the local stability of the co-existence equilibrium point.]]>
<![CDATA[Actuarial Modeling of COVID-19 Insurance ]]>
<![CDATA[Kurniawaty, Mila]]>;
<![CDATA[Arifin, Maulana Muhamad]]>;
<![CDATA[Kurniawan, Bagus]]>;
<![CDATA[Sukarno, Sadam Laksamana]]>;
<![CDATA[Prayoga, Muhammad Teguh]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.14999
<![CDATA[In this article, we provide an actuarial model expected to be able to help financial arrangements to cover losses due to the outbreak of coronavirus disease (COVID-19). We construct the dynamical models of premium and benefit based on generalized SEIR (Susceptible-Exposed-Infected-Recovered). Based on its dynamical model, we formulate the premium and the premium reserves on hospitalization and death benefits of the COVID-19 insurance.]]>
<![CDATA[Discriminant Analysis for Determination of Early Childhood Education Accreditation In Southeast Sulawesi Province ]]>
<![CDATA[Makkulau, Makkulau]]>;
<![CDATA[Wibawa, Gusti N.A.]]>;
<![CDATA[Ampa, Andi Tenri]]>;
<![CDATA[Pannangngareng Makkulau, Andi Tenri]]>;
<![CDATA[Harini, Sri]]>;
<![CDATA[Mulyanto, Angga Dwi]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v8i2.17404
<![CDATA[Discriminant Analysis is a statistical analysis that can classify cases on independent variables into groups or categories of dependent variables. The main objective of this research is classify eight indicators of the National education standards (SNP) early childhood and classify the accreditation value of early childhood (PAUD) in Southeast Sulawesi Province. The method used in this study used discriminant analysis. Accreditation value factors used in this study include Standards for Child Development Achievement Levels (X1), Content Standards (X2), Process Standards (X3), Standards for Educators and Education Personnel (X4), Facilities and Infrastructure Standards (X5), Management Standards (X6), Financing Standards (X7) and Education Assessment Standards (X8). Based on the results of data analysis, 8 SNP Indicators qualify as a form of discriminant equation model and accreditation value obtained based on the calculations of the National accreditation organization (BAN) PAUD and Non Fromal Education (PNF) Southeast Sulawesi are classified as follows: there are divided into 3 classifications, namely Accreditation C is 91.7%, Accreditation B is 85.1%, and for Accreditation A is 100%. So, the accuracy of the classification is 87.5%.]]>
<![CDATA[The Reflexive H-Strength on Some Graphs ]]>
<![CDATA[Sullystiawati, Lusia Herni]]>;
<![CDATA[Marsidi, Marsidi]]>;
<![CDATA[Putra, Eric Dwi]]>;
<![CDATA[Agustin, Ika Hesti]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v9i1.23172
<![CDATA[Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G). The irregular reflexive -labeling is defined by the function and such that if and if , where max . The irregular reflexive labeling is called an -irregular reflexive -labeling of the graph if every two different sub graphs and isomorphic to it holds , where for the sub graph . The minimum for graph which has an -irregular reflexive -labelling is called the reflexive strength of the graph and denoted by . In this paper we determine the lower bound of the reflexive strength of some subgraphs, on , the sub graph on the sub graph on and the sub graph on .]]>
<![CDATA[On the Dominant Local Resolving Set of Vertex Amalgamation Graphs ]]>
<![CDATA[Umilasari, Reni]]>;
<![CDATA[Susilowati, Liliek]]>;
<![CDATA[Slamin, S]]>;
<![CDATA[Prabhu, Savari]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.18891
<![CDATA[Basically, the new topic of the dominant local metric dimension which be symbolized by Ddim_l (H) is a combination of two concepts in graph theory, they were called the local metric dimension and dominating set. There are some terms in this topic that is dominant local resolving set and dominant local basis. An ordered subset W_l is said a dominant local resolving set of G if W_l is dominating set and also local resolving set of G. While dominant local basis is a dominant local resolving set with minimum cardinality. This study uses literature study method by observing the local metric dimension and dominating number before detecting the dominant local metric dimension of the graphs. After obtaining some new results, the purpose of this research is how the dominant local metric dimension of vertex amalgamation product graphs. Some special graphs that be used are star, friendship, complete graph and complete bipartite graph. Based on all observation results, it can be said that the dominant local metric dimension for any vertex amalgamation product graph depends on the dominant local metric dimension of the copied graphs and how the terminal vertex is constructed]]>
<![CDATA[Bühlmann's Credibility Model with Claims of Negative Binomial and 2-Poisson Distribution ]]>
<![CDATA[Maulidi, Ikhsan]]>;
<![CDATA[Apriliani, Vina]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.16400
<![CDATA[One of the premium determination techniques is to use credibility theory. In this study, a credibility premium determination model was derived with the best accuracy approach in the form of Bühlmann’s credibility premium. The claim data is assumed to have a Negative Binomial and 2-Poisson distribution. Bühlmann's credibility premium formula is given explicitly for these two data distributions. The obtained model is also applied to the correct data following these distributions. From the simulation results, it is obtained that the premium values are very close in value so that both models can be applied to the data and have a high level of credibility because they have a high credibility factor value.]]>
