Statistical Modeling of Some Cancerous Diseases Using the Laplace Transform Approach of Basic Life Testing Issues

Abstract

The purpose of the nonparametric statistical test used in this study is to compare different treatment options by looking at failure behavior in recorded survival data. Patients’ survival times are documented after using the proposed approach. The observed data’s behavior was assumed to be based on used better than aged in the moment generating function order (UBAmgf) characteristic or a constant failure rate in this study (exponential scenario). Suppose that the survival data is UBAmgf, then the treatment or the machine or system in use produces a better or a higher expected total present value than an older machine governed by an exponential survival function; if the data is exponential, the suggested treatment strategy is ineffective (the recommended treatment approach has neither positive or negative effects on the patients). To guarantee that the suggested statistical test is used correctly, the efficiency and critical values are calculated and compared to those of other tests, and the technique is then applied to medical data.

A Semi‐Analytical Solution of Inverse Laplace Transform

“…is is useful when the exact solution is unknown. For many engineering problems [18][19][20][21][22][23], medicine problems [24], and integro-differential equations of second-order problems [25][26][27], this method might be useful.…”

On basic life testing issues in medical research using non‐parametric hypothesis testing

“…Suppose that the following random sample $${X_1},{X_2}, \ldots ,{X_n}$$ was taken from F to apply this non‐parametric testing. Several authors have introduced non‐parametric hypothesis testing for a variety of life distributions (Bakr et al., 17 Mansour, 18 Abu‐Youssef and El‐Toony, 19 EL‐Sagheer et al 20 . and Mahmoud et al 21 .…”

Modeling Various Survival Distributions using a Nonparametric Hypothesis Testing Based on Laplace Transform Approach with Some Real Applications

“…We apply the conclusions in this work to certain real data sets to demonstrate their utility. We apply the data presented in bakr et al [1] (see Table 6), which represents the ages of the 40 patients with leukemia, taken in years.…”

“…We apply the data presented in bakr et al [ 1 ] (see Table 6 ), which represents the ages of the 40 patients with leukemia, taken in years.…”

“…Various life distribution classes have been proposed during the last century to model various elements of aging. See, for example, the studies of Bakr et al [ 1 ], Navarro and Pellerey [ 2 ], Bakr et al [ 3 ], Navarro [ 4 ], Qureshi and Kumar [ 5 ], and Qureshi and Yusuf [ 6 ], for definitions and preservation of several classes of life distributions, such as IFR, NBU, UBA, UBAmgf, NBUE, and their duals.…”